THESIS ON ANALYSIS AND DESIGN OF OVERHEAD TANK FROM …

THESIS ON ANALYSIS AND DESIGN OF OVERHEAD TANK

FROM WIND LOAD

IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE (M.Sc.) IN STRUCTURAL

ENGINEERING

BY

Menbermariam Woldeyesus

ADDIS ABABA, ETHIOIPIA

July 2016

A THESIS SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES OF

ADDISABABA SCIENCE AND TECHNOLOGEY UNIVERSITY IN PARTIAL

FULLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER

OF SCIENCE (M.Sc.) IN STRUCTURAL ENGINEERING

Approved by Board of Examiners

Dr. Suresh Borra ______________________ ____________________

Advisor Signature Date

Dr.Ing. Temesegne Wondimu _____________________ ____________________

External Examiner Signature Date

Dr. Mesay Daniel _____________________ ____________________

Internal Examiner Signature Date

Ato: Yesuf Esleman ______________________ ____________________

Chairman Signature Date

Declaration

I, the undersigned, declare that this thesis is my Original work and all sources of materials used

for the thesis have been duly acknowledged.

Name: Menbermariam Woldeyesus

Signature: ____________________

Place: Addis Ababa Science and Technology University

Date of submission: July, 2016

i

ACKNOLEDGEMENT

Thanks to God for each and every success in my life and satisfactory accomplishment of this

project. He was endowed me courage and strength as well as precious health throughout my

school time and entire life as well.

I would like to extend my deepest gratitude and heartfelt appreciation to my advisor Dr. Suresh

Borra Associate Professor of Bahirdar University for his advice, guidance, continuous follow

up, unreserved encouragement and constructive comments on the project that enabled the author

to grasp the necessary skill from the project with in short time

I also want to thank Dr. Habtemu Hailu, Dr. Habtemu Itefa and Dr. Mesay Daniel for their

unconditional support from the beginning up to completing master program course.

I want to express my gratitude to all Drs. who had given post graduate courses. And also I

would like to express my warm gratitude to my wife for life long support Wro. Wagaye Bekele,

and children Yoseph and Dawit, and for my sister Wro. Woderyelesh Zeleke, who has given a

special support in writing the whole thesis, And also for my brother Ato Gebreegziabher

Gebretsadik (G.G.) who has also rendering special support and follow up to enable me to

accomplish my thesis work.

I want to thank my sponsor ship Ethiopian Road Authority (ERA) Financing, facilitating and

attaining master program.

Finally, I am also gratefully acknowledging the contributions of all those individuals who had

contributed in one or the other way.

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List of Tables:

Table1.0 Loading conditions

Table6.0 Value of air density

Table6.1 Wind load on various elements

Table6.2 Size of the various members

Table6.3 Steel reinforcement

Table7.0 Dimensions of the tank from the wind analysis

Table7.1 Weight of the elements of the tank

Table7.2 H/R ratio

Table7.3 Type -1 Spectrum for „B‟ class soil

Table7.4 Importance factor for tanks

Table8.0 Moment coefficients in circular girders supported on columns

Table 8.1 Load pattern definition

Table 8.2 Load case definition

Table 9.1 Bracing beam forces for label 1

Table 9.2 Column forces for label 475,477, and 479

Table 10.1 Design values

Table 10.2 Load combination

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List of Figures:

Figure1.0 Types of Intze Tanks

Figure3.0 Components of the Intze water tank

Figure3.1 Sectional location of various forces

Figure3.2 Variation of meridional thrust over a sectional dome

Figure3.3 Forces acting on the unit length of the ring

Figure3.4 Loads at the junction of the ring beam B3

Figure3.5 Loads on the bottom dome

Figure3.6 Forces at the ring beam B2

Figure4.0 Tank supported on two columns

Figure4.1 Deflected shape of the two columns supported staging

Figure4.2 Staging subjected to wind

Figure4.3 Wind force on three or more columns staging

Figure4.4 Columns arranged symmetrically on a circle of radius “R”

Figure4.5 Different patterns of staging

Figure6.1 Graphs

(a) Wind force Vs staging height

(b) Variation of wind with respect to capacity

Figure7.0 Dimensions of the various members

Figure7.1 Base shear comparison for wind and earth quake

Figure7.2 Overturning moment comparison for wind and earth quake

Fig8.1 Concrete material definition

Figure 8.2 Reinforcement bar definition

Figure 8.3 Idealized rebar stress-strain profile

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Figure 8.4 Beam definition

Figure 8.5 Stiffness modifier

Figure 8.6 Column definition


Figure 8.8 Area element definition in SAP 2000


Figure 8.10 Response spectrum function definition

Figure 8.11 Load combination

Figure 8.12 Column and bracing beam model

Figure 8.13 Conical dome

Figure 8.14 Bottom dome

Figure 8.15 Cylindrical shell

Figure 8.16 Top dome

Figure 9.1 Column label

Figure 9.2 Bracing beam @ 5.75m





Figure 9.7 Un-deformed shape

Figure 9.8 Deformation due to full lateral water pressure

Figure 9.9 Deformation due to half lateral water pressure

Figure 9.10 Deformation due to wind load

Figure 9.11 Deformation due to earthquake

Figure 9.12 Deformation due to modal (mode-2)

Figure 10.1 Longitudinal reinforcement

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Figure 10.2 Shear reinforcement

Figure 10.3 Detail design calculation

Figure 11.1 Container detail

Figure 11.2 Column detail

Figure 12.1 Foundation model

Figure 12.2 Loading value

Figure 12.3 Settlement of foundation in mm

Figure 12.4 Soil pressure distributions

Figure 12.5 Reinforcement in X-direction (Bottom)

Figure 12.6 Reinforcement in X-direction (Top)

Figure 12.7 Reinforcement in Y-direction (Bottom)

Figure 12.8 Reinforcement in Y-direction (Top)

Figure 12.9 Flexural reinforcement of beam

Figure 12.10 Shear reinforcement of the beam

Figure 13.0 Moment coefficients

vi

TABLE OF CONTENTS

Page I Acknowledgment

Abstract XI

CHAPTER ONE 1

1. INTRODUCTION 1

1.0. Introduction 1

1.1 .Need of study of water tank 1

1.2. Classification of water tanks 2

1.2.1. General classification 2

1.2.1.1. Tanks resting on ground 2

1.2.1.2. Elevated tanks supported on staging 2

1.2.1.3. Underground tanks 2

1.2.2. Classification based on shape

1.2.3. layout of overhead tanks

2

3

1.2.4. Classification and layout of elevated tanks 3

1.3. Intze tank 3

1.4. Load combination 4

1.4.1. Imposed load 4

1.4.2. Wind load 4

1.5. Statement of problem 5

1.6. Objective 5

1.6.1. General objective 5

1.6.2. Specific objective 5

1.7. Methodology 5

1.8. Scope 6

1.9. Limitation 6

1.10. Literature review 7

vii

CHAPTER TWO 9

MATERIALS USED and THEIR DESIGN REQUIREMENT 9

2.1. Concrete 9

2.2. Steel 10

2.3. Minimum reinforcement 10

2.4. Concrete cover 11

CHAPTER THREE 12

ANALYSIS and DESIGN of INTZE TANK 12

3.0. Introduction 12

3.1. Analysis and design of elevated water tank 12

3.1.1. Member analysis 14

3.1.2. Top Dome and Top ring beam 14

3.1.3. Hoop stress 17

3.2. Design of R.C domes 19

3.2.1. Placement of main reinforcement in dome 19

3.3. Provision of ring beam 20

3.4. Provision of openings 20

3.5. The cylindrical portion of tank 20

3.6. Ring beam 21

3.7. Bottom dome 21

3.8. Bottom ring beam 23

CHAPTER FOUR 24

STAGING 24


4.1. Design of elevated tanks 24

4.1.1. Design of tank 24

4.1.2. Design of staging Reinforcement 24

4.2. Design of columns 25

viii

4.2.1.Wind loads 25

4.2.2. Axial forces in column 25

4.3. Design of tank supporting 25

4.3.1. Case 1 26

4.3.2. Case 2 28

4.3.3. Case 3 30

4.3.4. Case 4 31

4.4. Bracing 32

4.5. Force in braces 33

CHAPTER FIVE 34

JOINTS 34


5.1. Common joints in water tanks 35

5.1.1. Movement joints 35

5.1.1.1. Contraction joints 35

5.1.1.2. Expansion joint 36

5.1.1.3. Sliding joints 36

5.1.2. Construction joints 36

CHAPTER SIX 37

COLUMN FOUNDATION 37


6.1. Problem statement 38

6.2. Wind data 38

6.3. Staging 39

6.4. Wind forces from pressure 40

6.5. Roughness coefficient 42

6.6. Topography coefficient 43

6.7. Exposure coefficient 43

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CHAPTER SEVEN 48

EARTH QUAKE 48


7.1. Height of the C.G. of empty container 54

7.2. Seismic responses 55

7.3. Fundamental requirement according to EBCS 8 57

7.4. Seismic zones 57

Chapter Eight 61

Modeling 61


8.1. Material definition 61

8.2. Frame section definition 63

8.3. Area element definition 65

8.4. Load and combination definition 66

8.5. Modeling 68

Chapter Nine 71

Analysis Result 71


9.1. Labeling of elements 74

9.2. Results 76

9.2.1. Beam and Column forces 76

9.2.2. Deformed shapes 82

Chapter Ten 85

Design of Column 85


10.1. Design of column 86

10.1.1. Longitudinal design of column 86

10.1.2. Transverse reinforcement 87

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Chapter Eleven 90

Detailing 90

11.0. Container tank detail 91

11.1. Column detail 92

Chapter Twelve 92

Foundation Design 92


12.1. Modeling 92

12.2.Result 93

12.2.1. Settlement 93

12.2.2. Soil pressure distribution 94

12.3. Design 94

12.3.1. Mat reinforcement 94

12.3.2. Beam Design 95

Discussions 97

Conclusion 99

Appendix 100

Reference

101

xi

ABSTRACT

Reinforced concrete tanks are used liquid containing vessels. Such tanks can be

ground supported tanks ground storage reservoir and high ground level storage

reservoir or elevated water tanks may be referred as elevated storage reservoir.

Although most design codes provide guidelines for rectangular and cylindrical

tanks, no guidance is provided in EBCS codes for Elevated water tanks. For the

analysis and designing the Intze tank along with the EBCS code, ACI code and IS

code is used. Therefore, this thesis is study the behavior and design of this type of

tanks. In areas with high probability of natural disasters, ability of lifeline systems

to resist disaster related damages is one of the most important civil engineering

challenges. Elevated water tanks are one of the most important lifeline structures.

In this thesis an extensive computational study has been conducted to find out

the performance of elevated Intze water tank under wind force. Since these

structures have large mass concentrated at the top of slender supporting

structure, these structures are especially vulnerable to horizontal forces due to

wind. Elevated water tanks are analyzed with different parameters to study the

effect of capacity, height of staging, terrain category and wind zone. Findings of

the present study shall lead us to better understanding of the behavior of

elevated water tank under wind load and safer design of such structure. In doing

the design the working stress methods and limit state design is used based on the

requirement. In this study membrane analysis is used to find the meridional

thrust and hoop stress calculation at various components of the Intze tank.

KEYWORDS: Life line systems, Intze tank, Meridional thrust, Hoop stress, EBCS,

ACI, IS codes, Wind load

1

CHAPTER-I

INTRODUCTION

1.0. Introduction

Water is basic human needs for daily life sufficient water distribution depends on design of a

water tank in certain area. Water supply is a life line facility that must remain functional even if

disaster occurred. Elevated water tank is a water storage container constructed for the purpose

of holding a water supply at a height sufficient to pressurize a water distribution system. In

major cities the main supply scheme is augmented by individual supply systems of institutions

and industrial estates for which elevated tanks are an integral part. Also at the times of cyclone

it was observed that the storage tanks were displaced by few meters and some were

overturned due to wind. They were swept away by the wind. Flying debris caused dents on the

surfaces when they hit the tanks. So it is important to check the severity of these forces for

particular region.

The study of damage histories revealed damage/failure of reinforced concrete elevated water

tanks of low to high capacity. Damage of the important lifeline facility like elevated water tanks

often results in significant hardships even after the occurrence of the disaster, claiming human

casualties and economic loss to build environment. Investigating the effects of wind has been

recognized as a necessary step to understand the natural hazards and its risk to the society in

the long run. Most water supply systems in developing countries, such as Ethiopia, depend on

reinforced cement concrete elevated water tanks. The strength of these tanks against lateral

forces, such as those caused by wind, needs special attention.

A water tower also serves as a reservoir to help with water needs during peak usage times. A water tower is an elevated structure supporting a water tank constructed at height sufficient to pressurize a water supply system for the distribution of potable water and to provide emergency storage for fire protection .In some places the term stand pipe is used interchangeably to refer a water tower especially one with tall and narrow proportions. Water towers are able to supply water even during power outages because they rely on hydrostatic pressure produced elevation of water (due to gravity) to push the water into domestic and industrial water distribution systems.

1.1. Need for study of Water Tanks 1) Water tanks are visually simple but structurally difficult

2) Difficult to take the load cases and load combinations

3) Distribution of stress in the structure

4) Distribution of mass

5) Hydro dynamic effects

6) Very critical problem is the slab and beam joints

2

1.2. Classification of water tanks

1.2.1. In general water tanks can be classified under 3-heads

1) Tanks resting on ground

2) Elevated tanks supported on staging and

3) Underground tanks.

1.2.1.1. Tanks resting on ground

These are used for clear water reservoirs, settling tanks, aeration tanks etc. these tanks directly

rest on the ground. The walls of these tanks are subjected to water pressure from inside and

the base is subjected to weight of water from inside and soil reaction from underneath the

base. The tank may be open at top or roofed

1.2.1.2. Elevated tanks supported on staging

These tanks are supported on staging which may consist of masonry walls, R.C. tower or R.C.

column braced together- The walls are subjected to water pressure from inside. The base is

subjected to weight of water, weight of walls and weight of roof. The staging has to carry load

of entire tank with water and is also subjected to wind loads.

1.2.1.3. Underground tanks

These tanks are built below the ground level such as clarifier’s filters in water treatment plants,

and septic tanks .The walls of these tanks are subjected to water pressure from inside and earth

pressure from outside. The base of the tanks is subjected to water pressure from inside and soil

reaction from underneath. Always these are covered at top. These tanks should be designed for

loading which gives the worst effect.

The design principles of underground tanks are same as for tanks resting on the ground. But the

walls of the underground tanks are subjected to internal water pressure and outside earth

pressure. The section of wall is designed for water pressure and earth pressure acting

separately as well as acting simultaneously.

1.2.2. Classification of water tanks based on shape

1) Circular tanks

2) Rectangular tanks

3) Spherical tanks

4) Intze tanks and

5) Circular tanks with conical bottoms.

3

1.2.3. Layout of overhead tanks

Generally the shape and size of elevated concrete tanks for economical design depends upon

the functional requirements such as

i) Maximum depth of water

ii) Height of staging

iii) Allowable bearing capacity of foundation strata and type of foundation suitable

iv) Capacity of tank and

v) Other site conditions.

1.2.4. Classification and layout of elevated tanks

Based on the capacities of the tank the possible classification for types of elevated tanks may be

as followed as given below for general guidance.

a) For tank up to 50m3 capacity may be square or circular in shape and supported on

staging on three or four columns.

b) Tank capacity above 50 m3 and up to 200m3 may be square or circular in plan and

supported on minimum four columns.

c) For capacity above 200m3 and up to 800 m3the tank may be square, rectangular, circular

or Intze type tank. The number of columns to be adopted shall be decided based on the

column spacing which normally lies between 3.6 and 4.5m

For circular, Intze or conical tanks a shaft supporting structures may be provided

1.3. Intze Tank:

The Intze principle is a name given to two engineering principles both named after the hydraulic

engineer Otto Intze. In the one case the Intze principle relates to a type of water tower, in the

other a type dam.

Circular tanks with flat bottom as well as with domical bottom:

In the flat bottom the thickness and reinforcement is found to be heavy. In the domed bottom

though the thickness and reinforcement in the dome is normal, the reinforcement in the ring

beam is excessive.

Therefore in the cases of large diameter tanks and economical alternative would be to reduce

its diameter at its bottom by conical dome. Such a tank is known as Intze tank and is very

commonly used. The main advantage of Intze tank is that the inward radial thrust of the conical

bottom balances the outward radial thrust of the spherical bottom. Water tanks designed on

the Intze principle

4

W.L W.L W.L

a: Intze 1 Tank b: Intze 1 tank with inside cylinder

W.L

c: Intze 2 Tank

Fig.1.0.Types of Intze tanks.

1.4. Load combinations

Design of liquid retaining structures involves decisions to be made by the engineer based on

rules of thumb, judgment, code of practice and previous experience.

1.4.1. Imposed loads

Weight of water may be taken as live load for members directly continuing the same. The

weight of water shall be considered as dead load in the design of staging.

1.4.2. Wind load

Wind shall be applied according to EBCS. While analyzing the stresses the combination shall be

as follows.

a) Wind load with empty tank and

b) Wind load with tank full.

The worst combination of the stress on account of the above shall be considered while working

out the permissible stresses.

5

The following are the loads and loading conditions which prevail over R.C. water tank

No

Loads

Influence of load on chimney/staging

1. Dead Load Static

2. Live Load Static+ Dynamic

3. Wind Load Static+ Dynamic

4. Thermal stress Static

5. Seismic Load Static+ Dynamic

Table 1.0. Loading conditions

1.5. Statement of Problem

Lack of expertise in analyzing and designing of elevated water tanks in Ethiopia, The present

study is an effort to standardize the analysis and design of this.

1.6. Objective

1.6.1. General objective

The main objective of this study to identify the dynamic behavior of elevated water tank

under wind load.

1.6.2. Specific objectives

To develop and use the formula for membrane stresses in shells;

To analyze the stresses in the roof and bottom domes of the tank, the conical section

and cylindrical section’

To analyze the staging from wind load point of view at different heights of staging ; and

To develop response curves.

1.7. Methodology

A detailed literature study is done to look into the background of various concepts in

previous studies.

To analyze and design of Intze water tank using EBCS 1995(1, 2, 8), American concrete

institute and Euro code (2, 8) 2004.

Analysis is done by the finite element software SAP 2000 for earthquake

Produce graphical representation is done wherever required

6

1.8. Scope

The scope of this research is limited to understanding the behavior of elevated water tanks

subjected to dynamic loads such as wind loads and fully study and analyze the membrane

theory of shells because the roof and bottom domes of an Intze tank are spherical domes with

the shell thickness small compared with the other dimensions and with the radii of curvature.

1.9. Limitations

This study is not included the soil structure interaction

Limited to study wind load for different elevations but not for different bearing capacity

of soils

It is assumed that the sloshing wave height is negligible. Sloshing is defined as the

periodic motion of force liquid surface in partially filled containers. It is caused by any

disturbance of partially filled liquid containers. Sloshing results additional hydrodynamic

pressure.

7

1.10. Literature Review

Up to now many researchers had been contributed on overhead water tank from wind load and

earthquake. Therefore the published journals of them are now as references

Manoranjan shoot and Tandrita bitwise (2007): Study on water tanks in the Kutch region of

Gujarat (India) after that area subjected to the earthquake

They have found in that the tanks in majority of the cases they were designed for the

wind load but they were not checked for the earthquake load by assuming that the

tanks will resist the earthquake load once they are designed for the wind load.

They were concluded type of staging is good for resisting the later loads like wind and

earthquakes.

The frame type staging is superior to the shaft type of the staging because the frame

types of staging have many flexural members that are provided in the form of columns

and braces.

Akshya B.Kamdi and R.V.R.K. Prasad (2012):

Their contribution in relation to circular water tanks is theory behind the usage of the

limit state method and working stress methods and also specified the necessity of the

calculation of the crack width.

Pathway: Artificial neural networks were used in predicting the cost of Intze and circular tanks

Mohammed: Application of optimization method to the design of storage tanks was done by

Saxana: Heuristic flexible tolerance method based on the Indian and ACI (building 1969) codes for achieving minimum cost design of an Intze type R.C.C tank presented by.

Jan: A direct search method and the SUMT was used by Jan for finding out minimum cost

design of a R.C.C cylindrical water tank based on the British code for water tanks.

Dr. Manoj Hedaoo & Dr. Suchita Hirde [2011]: On the study of seismic performance of the

elevated water tank for various seismic zones of India for various heights and capacity of

elevated water tanks for different soil conditions

The effect of height of water tank, earthquake zones and soil conditions on earthquake

forces have been presented in this paper with the help of analysis of 240 models of

various parameters.

8

The study is carried out on RCC circular elevated water tank with C-20 grade of concrete

and Fe-415 grade of steel & SMRF are considered for analysis.

Elevated water tank having 50,000 liters and 100,000 liters capacity with staging height

12 m. 16 m, 20 m, 24 m, 28 m considering 4 m height of each panels are considered for

the study.

Author has given following conclusions from his analysis

Seismic forces are directly proportional to the Seismic Zones,

Seismic forces are inversely proportional to the height of supporting system,

Seismic forces are directly proportional to the capacity of water tank, and

Seismic forces are higher in soft soil than medium soil, higher in medium soil than hard

soil. Earthquake forces for soft soil is about 40-41% greater than that of hard soil for all

earthquake zones and tank full and tank empty condition.

Now a days the population growth of urban area of Ethiopia increases. Because of this the

demand of sufficient and clean water supply at peak hour and during power shortage time is

very crucial.

To minimize this problem high raised, large and Intze shape of overhead tanks are a

better choice for pressurized a water distribution system.

9

CHAPTER-2

MATERIALS USED AND THEIR DESIGN REQUIREMENTS

2.1. CONCRETE

Reinforced concrete structures are of different because the design of liquid retaining

structure is different from an ordinary R.C. Structure as it is required that the concrete

should not crack. In order to make the liquid retaining structure efficient working it should be

of high strength and quality and should be leak proof. The design of the concrete mix should be

done in such a manner that the resultant concrete is sufficiently impervious. Also at compaction

level efficient compaction preferably by vibration is essential. Therefore the thoroughly

compacted concrete permeability is dependent upon water cement ratio. Water cement ratio

and permeability are directly proportional that is Increase in water cement ratio increases

permeability, while concrete with low water cement ratio is difficult to compact. Thus water

cement ration is to chosen in such a manner that the compacted concrete have sufficient

permeability and good workability. The maximum free water cement ratio for liquid retaining

structures shall be 0.45 for reinforced concrete and 0.50 for plain concrete. Lower water

cement ratio may be achieved by us in suitable admixtures like plasticizers or super plasticizers.

The Amount of such plasticizer shall not be more than 2% by mass of cementations material

(I.S: 10262-2007), i.e., sum of mass of cement and additives.

Not only had the above said the other causes are also there for leakage in concrete. They are

defects such as segregation and honey combing. Along these joint should be given proper care.

Because all joints should be made water-tight as these are potential sources of leakage. Over

these certain measures will help to make the water retaining structures to be efficient. Use of

small size reinforcement bars placed properly, leads to closer cracks with smaller width. The

risk of cracking because of temperature and shrinkage effects may be minimized by limiting

the changes in moisture content and temperature to which the structure as a whole is

subjected. To control the shrinkage and thermal movements’ provision of joints deserves extra

special attention in case of liquid retaining structures.

Generally concrete mix weaker than C-30 is not used. Considering the concept of durability of

water retaining structures this is the minimum grade of concrete. In order to get high quality

and impervious concrete, the proportion of cement, fine and coarse aggregate to is determined

carefully and water cement ratio is adjusted accordingly. Finally depending up on the exposure

conditions of the structure, the grade of concrete is decided .Minimum cement content

excluding the additives like fly ash and granulated slag shall not be more than 400 kg/m3 to

safeguard against cracking due to drying shrinkage.

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2.2. STEEL

Since concrete and steel are assumed to act together, therefore it is required to check the

stresses in the steel and concrete. From concrete point of view it has to be checked to avoid

cracks in concrete whether the tensile stress in concrete is within limits or not .On the other

hand the tensile stress in steel will be limited by the requirement that the permissible tensile

stresses in concrete is not exceeded. For calculation of strength the permissible stresses in

steel reinforcement is as follows.

(a) Permissible tensile stresses in member in direct tens = 1500 Kg/Cm2

(b) Tensile stress in member in bending

On liquid retaining face of member = 1500 Kg/Cm2

On faces away from liquid for members less than 225 mm thick = 1500.Kg/Cm2

(c) On faces away from liquid for members 225 mm. thick or more = 1900 Kg/Cm2

2.3. Minimum Reinforcement

Minimum reinforcement is based on the surface zones of the member. When the thickness of

the member is up to 500 mm, i.e., , assume each surface zone to be of thickness

equal to

. When the thickness of the member exceeds 500mm assume each surface zone of

250mm thickness and the internal concrete shall be ignored for the purpose of the minimum

reinforcement calculations. Minimum reinforcement in walls, floors and roof in both the

perpendicular directions shall not be less than 0.35% of the surface zone cross section for HYSD

bars and not less than 0.64% for mild steel bars. If the length the member is less than 15 m

these reinforcement can be reduced to 0.24% for HYSD bars and 0.4% for mild steel bars. If the

thickness of the wall is less than 200mm, the calculated reinforcement may all be placed on one

face.

For slabs up to 500mm depths all the steel calculated shall be provided equally on both sides.

This steel is required against temperature strain across the depth of the slab. Temperature

strains are much smaller at the center of depth. Therefore for the depth more than 500 mm the

central part is ignored. Thus for slab depth more than 500mm, the minimum reinforcement

remains constant with depth at both faces. The spacing of the bars shall not be greater than

300mm or thickness of the section. And also permissible stresses in steel in working stress

method are reduced to decrease the tendency of cracking.

The area of the reinforcement shall be such that when crack forms the reinforcement shall be

able to absorb the total force. If the steel ratio is lower the ultimate concrete strength will be

11

more than strength of steel. If crack forms the steel will yield and will not be able to properly

restrain the crack width. On the other hand if steel ratio is more the steel will not yield and

resist all tensile force leading to limited crack width.

In the circular part of the tank hoop steel is main steel (horizontal) and is circular in shape. And

the other one vertical is the distribution steel. In order to reduce the labor of fixing the

reinforcement horizontal steel will be placed in outer layers. Therefore the horizontal steel

should be properly curved in a hooping machine and not bent series of kinks. And also one bar

cannot be used continuous for perimeter of the wall. Therefore lapping of bars is necessary.

For an ordinary slab or beam generally lapping is done at the place where stresses are reduced

to 50%. In circular portion of the tank walls, at all the sections of the horizontal bar the stress is

the same. Therefore it is preferable to carefully plan the splicing of reinforcement to see that

splices are very well staggered. In the case of lapping the lap length should be equal to . As

usual all the bars should not be staggered at one section and should be staggered. It should be

taken care that at any vertical section not more than one bar in three bars should be lapped. At

any vertical section axial tension is shared by concrete and steel, however at the vertical joint

only steel resists tension and therefore steel is provided to carry all the tension. The bars

should not be lapped at or near the vertical joint.

2.4. Concrete cover

For liquid retaining structures, the exposure is considered to be “severe”. The minimum

concrete cover to the reinforcement shall be 45 mm.

12

CHAPTER-3

ANALYSIS and DESIGN INTZE TANK

3.0. Introduction

Working stress method and Limit state method

The working stress method of design was evolved around 1900. Although this method have

been performing its function satisfactorily since a long time but this method of design results in

a larger percentage of steel and uneconomic sections. However the working stress method is

the only method available to check the R.C sections against failing in service stresses and

serviceability states of deflection and cracking. But the modern methods i.e., limit state design

which is based on a semi probabilistic approach. Although this method provides much

economical and safe sections but it has not been formulated yet to suit the design of structures

like storage tanks. Limit state method allows higher strain in steel as well as in concrete which

creates the problem of cracking in R.C. structures. Hence working stress method is still used in

the design of tanks.

The components of the water tank (container) are designed by using working stress method.

Other related elements like columns, ties, stair (If provided of an R.C) designed according to the

limit state method.

3.1. Analysis and Design of elevated water tanks

This study has emphases merely on elevated water tank. Design of liquid retaining structures

has to be based on the avoidance of cracking in concrete regard to its tensile strength. It has to

be ensured that no cracks should be formed on the water face. The design of such tanks is done

in two ways.

1) Membrane analysis

2) Analysis taking into account of continuity effect at joints.

In the membrane analysis it was assumed that each member is independent of the other and

therefore subjected to direct stresses only and no bending moment is introduced. However due

to continuity of joints between the members joint reactions are introduced due to which

secondary stresses in the form of edge moment and hoop stresses are introduced in the

members. Stresses due to continuity can be obtained by applying the principle of consistent

deformations. At each joint the horizontal deformation and angular displacement between the

shells should be consistent

The analysis of Intze tank is therefore done in two stages

13

1) Membrane analysis in which membrane stresses in each member are calculated and the

members are designed

2) Analysis of effects due to continuity in which the deformations due to membrane

stresses are first calculated and equations of consistent deformations are formulated to

know the secondary stresses.

The final stresses are then found by adding the stresses due to the above two cases.

The main advantage of such a tank is that the outward thrust from the top of the conical part is

resisted by the ring beam B3 (showed in below figure), while the difference between inward

thrust from the bottom of the conical dome and the outward thrust from the bottom dome are

resisted by ring beam B2 (shown in below figure).

The Proportions of the conical dome and the bottom dome are so arranged that that the

outward thrust from bottom dome balances the inward thrust due to the conical dome.

The below figure suitable proportions for Intze tank with internal diameter “D”. The volume of

water stored in the tank with those proportions is 0.585D3

In general the volume of water stored is given by

(

)

( )

Top Dome Radius R1 h1 B1 (Ring Beam)

Cylindrical portion

D=2R

h= (2/3) D B3 (Ring Beam)

ho= (3/16) D

Conical Dome h2=(1/8)D

Bottom dome radius R2 B2 (Circular beam)

Do= (5/8) D Columns

Fig.3.0. Components of Intze tank

14

From economical considerations the inclination of the conical dome should be with

the horizontal.

3.1.1. Membrane analysis

In the membrane analysis the members are assumed to act independent of the others. The

members are therefore subjected to only direct stresses and no B.M is introduced.

3.1.2. Top dome and Top Ring beam B1

A dome may be defined as a thin shell generated by the revolution of a regular curve about one

of its axes. The shape of the dome depends upon the type of the curve and the direction of the

axis of revolution. When the segment of curve revolves about its vertical diameter a spherical

dome is obtained

Similarly conical dome is obtained by the revolution of the right angled triangle about its

vertical axis. While the elliptical dome is obtained by the revolution of a right angled triangle

about one of its axes.

However out of these spherical domes are more commonly used. In case of a spherical dome

the vertical section through the axis of revolution in any direction is an arc of circle

Domes are used in variety of structures such as

1) Roof of circular areas

2) Circular tanks

3) Hangers

4) Exhibition halls, auditoriums and planetariums and

5) Bottoms of tanks , bins and bunkers

Nature of stresses in spherical domes:

1) A spherical dome may be imagined to consist of a number of horizontal rings placed

one over the other

2) The diameter of successive rings increases in the downward direction and the

equilibrium is maintained independently of the rings above it.

3) The circle of each ring is called latitude

4) The circle drawn through two diametrically opposite points on a horizontal diameter

and the crown is known as a meridian circle. All meridian circles converge at the crown

(or top most point) of the spherical dome.

The below (b) shows the vertical section of the spherical dome. The successive horizontal

rings subtend equal angle at the center of the sphere. The joint between successive

15

horizontal rings is radial. Every horizontal ring supports the load of the ring above it and

transmits it to the one below it. The reaction between the rings is tangential to the curved

surface giving rise to compression along the medians. The compressive stress is called

meridonial thrust or meridonial compression.

The below C shows the plan of a horizontal ring which may be imagined to consist of a

number of voussoirs. The joints between adjacent voussoirs of the ring are radial. The

tendency of separation of any voussoir will be prevented because of its wedge shape and

therefore hoop compression will be caused in each ring.

T

Ring T Ring

Frustum of a spherical Dome

a b

H

H Latitude T

H H

Meridian T Meridian

Plan of a Ring

c d

Fig.3.1. Sectional location of various forces

To summarize therefore two types of stresses are induced in a dome.

1) Meridonial thrust(T) along the direction of meridian

2) Hoop stress along the latitudes.

Analysis of spherical domes:

Let us now analyze stresses developed in a spherical dome of uniform thickness for uniformly

distributed load.

w- Uniformly distributed load inclusive of its own weight per unit area

16

r- Radius of the dome

t- Thickness of dome shell

T- Intensity of meridonial thrust

H- Intensity of hoop stress.

Meridionial Thrust:

The fig (4) shows the section through the vertical axis of revolution of a thin spherical dome

P T

A Q B

C D T+dT

r O

Fig.3.2. Variation of meridonial thrust over a sectional dome

Let us consider the equilibrium of a ring ABDC, between the two horizontal planes AB and CD.

The extremity of the horizontal plane AB makes an angle “ with the vertical at the center.

While the extremity of the horizontal plane CD makes an angle . The ring thus subtends

an angle at the centre.

The following are the forces acting on the unit length of the ring

1) The meridonial thrust “T” per unit length of the circle of latitude “AB” acting

tangentially at “B”( or at right angles to the radial line “OB”)

2) The reaction or thrust “T+dT” per unit length of circle on latitude “CD” acting

tangentially at “D”

3) The weight “ of the ring itself acting vertically down

17

T B

D

O

Fig.3.3. Forces acting on the unit length of the ring

It should be noted that the reaction “T+dT” will be greater than the thrust “T” due to the effect

of the weight of the ring and due to change in the inclination from " of . Of the

radial lines.

The meridonial thrust “T” is caused due to the weight of dome shell APB above the rotational

plane “AB”

Surface area of dome shell APB =( )( )

But

( )

Weight of dome shell above ( )( )

( ( )( )

( )

Since the sum of vertical components of thrust “T” acting along the circumference of the circle

of latitude must be equal to the total weight of the dome shell “APB” we have

( )( ) ( )

( ) ( ) ( )

( )

3.1.3. Hoop stress

We have seen the meridonial thrust “T” increases to “T+dT” at the bottom of the ring. This

difference in the meridonial thrust “T” and “T+dT” acting at “ and .respectively to the

horizontal causes hoop stress.

18

Let “H” be the hoop force per unit length of surface measured on a great circle arc:

Breadth of ring =

Hoop force =

The horizontal components of “T” is and this horizontal component cause hoop

tension tending to increase the diameter of the ring .While horizontal component of “T+dT”

will (T+dT) cos ( ) and this horizontal component cause hoop compression

Now magnitude of hoop tension = ( )

= ( ) ( )

Magnitude of hoop compression=( ) ( )

=( ) ( ) ( ) ( )

The difference between (1) & (2) specify the resultant stress

If 1 > 2---- hoop tensile

1 < 2------ hoop compression

Hence the limiting case when is extremely small

( )

But ( )

[

( )

]

*

+

*

+

*

+

( )

19

The above expression gives the hoop stress in any horizontal ring the extremity of which

subtends an angle “ with the vertical at the center. If the value of “H” obtained from above

equation is positive hoop force will be compressive otherwise it will be tensile.

At the crown , hence equation becomes

Intensity of hoop stress at crown is

(compressive), This is the maximum value of hoop

stress. The hoop stress goes on decreasing as “ increases till “H” becomes zero. After that “H”

becomes tensile.

To find the position of the plane where hoop stress becomes zero we have

( )

Hence round the circle of latitude at which the angle hoop stress is zero. For all

portion of dome about this angle hoop compression will be developed while for the portion

below this plane hoop tension will be developed which will go on increasing further towards

the base of the dome.

3.2. Design of R.C Domes

The requirements of thickness of dome and reinforcement from the point view of induced

stresses are usually very small. However a minimum thickness of 7.5 cm is provided to protect

the steel. Similarly minimum steel provided is 0.15% of the section area in each direction

meridonally as well as along the latitudes. This reinforcement will be in addition to the hoop

tensile stresses. The steel reinforcement is provided in the middle of the thickness of the dome

shell. Near the edges some hogging bending moment may be developed and hence meridonial

steel should be placed near the top surface.

For Cover slab: It may be flat or in domed shape. For small plan area, the cover slab may be flat,

however for large area, domes are economical

3.2.1. Placement of main reinforcement in dome

As stated earlier a minimum reinforcement of 0.15% of area is provided both in the direction of

latitude as well as of the meridians. If the reinforcement along the meridians is continued up to

crown there will be congestion of steel there. Hence from practical considerations the

meridonial reinforcement is stopped at any latitude circle near crown and a separate mesh is

provided. No separate reinforcement along latitude is provided in this area at the crown

20

3.3. Provision of ring beam

If the dome is not hemispherical the meridonial thrust at the supporting circle of latitude (i.e.,

at the base) will not be vertical. The inclined meridonial thrust at the support will have

horizontal component which will cause the supporting walls to burst outwards causing its

failure. In order to bear this horizontal component of meridonial thrust a ring beam is provided

at the base of the dome.

The reinforcement provided in the ring beam takes this hoop tension and transfer only vertical

reaction to the supporting walls. The tensile stress on the equivalent area of concrete on the

ring beam section should not exceed 12 N/mm2

3.4. Provision of openings

Openings may be provided in the dome as required from other functional or architectural

requirements. However sufficient trimming reinforcement should be provided all round the

openings as showed below. The meridonial and hoop reinforcement reaching the opening

should be well anchored to the trimming reinforcement.

If there is an opening at the crown of the dome and if there is any concentrated load of lantern

etc. acting there a ring beam should be provided at the periphery of the opening

The design is carried out as per relevant analysis procedures combined with Indian standard

codes of practices.

The water tank dome is designed by working stress method and the supporting columns and

braces by limit state method. The analysis account for all forces inside the dome arising out of

water retained and live loads including the external environmental forces of wind in addition to

ubiquitous dead loads.

The foundation forces at the level of safe bearing capacity are also evaluated and then

foundation design can be done.

3.5. The cylindrical portion of tank

Let the diameter of the tank “D” and the height of the cylindrical portion “H”. The walls are

assumed to be free at top and bottom. Due to this tank walls will be subjected to hoop tension

only without any bending moment, maximum hoop tension will occur at base, it’s magnitude

being equal to

per unit height. The tank walls are adequately reinforced with horizontal

rings provided at both faces .In addition to this vertical reinforcement is provided on both the

faces in the form of distribution reinforcement.

21

3.6. Ring beam B3 at the junction of cylindrical wall and conical dome

The vertical load at the junction of wall with conical dome is transferred to ring beam B3 by

meridional thrust in the conical dome. The horizontal component of this thrust causes hoop

tension at the junction. The ring beam is provided to take up this hoop tension

W-Load transmitted through tank wall at the top of conical dome per unit length

Inclination of conical dome with vertical

T- Meridional thrust in conical dome at the junction

W

B3 P3

T

B2

Fig.3.4. Loads at the junction of ring beam B3

3.7 .Bottom dome

Domes are economical than flat roofs for large spans. The bottom slab is divided into conical

dome and spherical dome in such a way that the inward thrust due to conical dome on bottom

most ring beam gets balanced by the outward thrust of the spherical dome. The inclination of

the spherical dome is usually 450to 550 with the vertical so as to obtain the net thrust as hoop

compression and not the hoop tension. The conical dome is used in order to reduce the

diameter of the spherical dome. And the diameter of the spherical dome is usually 65% to 75%

of the diameter of the tank. The top domes shall be designed for live load of1.5 KN/m2

Bottom dome develops compressive stresses both meridionally as well as along hoops due to

weight of water supported by it and also due to its own weight

Let be the total depth of water above the edges of the dome

The weight of water above the surface of the dome is given by

(

)

( )( )

22

W.L

Wo

Do Ho

h2

H2 R2 B2

F2

T2

Fig.3.5. Loads on the bottom dome

Where is the radius and

is the rise of the bottom dome

Total surface area of dome

Self-weight of dome ( )

Where is the thickness of bottom dome

Total load = ( )

Meridional thrust

Intensity of load

Maximum hoop stress at center =

Knowing the meridional thrust and hoop stress the dome can be designed.

23

3.8. Bottom ring beam B2

The ring beam receives an inward inclined thrust from the conical dome and an outward

thrust from the bottom dome. The horizontal components of both of these oppose each

other.

Net horizontal force “P” is given by.

To T2

B2

Fig.3.6. Forces at the ring beam B2

If > the beam will be subjected to hoop compression

If however it will be subjected to hoop tension

Therefore the dimensions of the tank should be so adjusted that either “P” is zero or “P” is

compressive.

The hoop force is given by

If b2 is the width and d2 is the depth of the ring beam the stresses is given by

The vertical load per unit length is given by

Per unit length.

The circular ring beam can now be designed for the above superimposed load.

24

CHAPTER-4

STAGING

4.0. Introduction

Height of staging is the difference between the lowest supply level of tank and the average

ground level at the tank site.

For small capacity say 40000 to 50000 liters tanks square in plan are economical. For large

capacity water tanks circular tanks prove economical. Among large capacity circular tanks, Intze

tanks are economical.

4.1. Design of elevated tanks

Structural design of an elevated water tank consists of:

i) Design of tank (container)

ii) Design of staging

iii) Design of foundation.

4.1.1. Design of tank

Design of tank: Design of water tank (container) consists of designing of elements like cover

slab, side walls, base slabs and beams.

4.1.2. Design of staging

The staging for elevated tanks is designed for the following loading conditions.

DL + LL + water load.

DL (Tank empty) +wind load.

DL + LL + water load+ WL

Analysis of Wind load is carried by either the exact methods or approximate methods like

portal frame method or cantilever method.

The columns are tied by tie beams for the following reasons:

1) In order to reduce the effective length of the columns.

2) In order to reduce the moments and shears caused due to horizontal loads.

3) Integral action is secured by tying all the columns.

25

Tie beams are to be designed for axial thrust, shears and moments. The axial thrust from gravity

loads shall be considered as 3% of the axial gravity loads in columns. This may be of tension or

compression. Forces because of the wind load are obtained from the analysis. As the wind may

reverse their directions the forces in the ties will be reversed. Therefore the reinforcement in

ties shall consist of top and bottom reinforcement equally distributed.

Staging- Columns and bracings:

Design of staging consists of design of columns and design of bracings. The design will be

carried out by using limit state method.

4.2. Design of columns

Gravity loads: Gravity loads on column consist of dead loads and water load. Thus loads on

column are determined for tank empty and tank full conditions.

4.2.1. Wind loads

The wind loads produce tension on windward columns, compression in leeward columns and

no axial force in columns on the line of neutral axis.

4.2.2. Axial forces in columns

Wind forces on windward side are calculated on container on columns and on bracings. To

determine the axial forces in columns, determine the sum of moments of all these forces about

the neutral axis at the bottom of the columns.

The staging acts as vertical cantilever supported at the base and subjected to the horizontal

wind forces.

4.3. Design of tank supporting towers

The designer before taking up the design should first decide the most suitable type of staging of

tanks and correct estimation of loads including statically equilibrium of structure particularly in

regard to overturning of overhanging members shall be made. The design is to be based on the

worst possible combination of load, moments and shears because of vertical loads and

horizontal loads acting in any direction when the tank is empty as well as full.

In order to obtain the desired head of water, water tanks are generally elevated above the

ground. This is accomplished either by supporting the tank on masonry walls provided up to the

desired height or by supporting it on a number of columns suitably braced at various heights.

In the latter case the columns are subjected to

26

1) Dead load of tank, water and other connected structures.

2) Wind loads or seismic forces.

Generally size of the all the columns are of equal dimensions and are placed symmetrically

.Therefore the dead load may be assumed to be equally distributed amongst the columns. The

force due to wind and other horizontal loads will depend upon the arrangement of columns and

their support conditions.

The loads from the water tank are transferred to the staging through the ring beam, and this

ring beam is supported by the columns (staging). Usually 4 to 12 columns are used in the

staging they are spaced at equidistance, therefore they share the gravity load equally. For 3

column staging the stresses are very high therefore it is rarely built. The columns may be

designed as vertical or with some batter, particularly for tall water tanks the staging is having

some batter. This may be in the range of 1:12 to 1.25:12. Wind force may act in any direction

but the wind force in the direction parallel to the diagonal works out to be critical. In the

columns the compression force develops because of tank loads and overturning moments

caused by wind.

We shall consider several cases and analyze them by approximate methods only

4.3.1. Case 1

Rows of columns (Two equal columns) with rigid top and fixed at the footings.

Below fig (9) showing that a tank supported on two equal columns .Let ”P” be the total wind

load on the tank surface. The columns are fixed at the base and are rigidly connected to the

tank.

H

L

Fig.4.0 Tank supported on two columns

27

Below figure shows the deflected shape.

P

H

O1 P/2 O2 P/2

h/2

MA A P/2 MB B P/2

V V

P/2 Ph/4

P/2

P/2 Ph/4

Shear Force Diagram Bending moment Diagram

Fig.4.1. Deflected shape of the tank supported on the two columns

The analysis is based on the assumption that the point of contra flexure (o1 and o2) occurs at

the mid height of each column. At the point of contra flexure there is no bending moment and

the column is subjected to only horizontal shear (Q) and axial force (V)

In general there are three effects of wind and other horizontal forces

1) Bending moment –M

2) Horizontal shear –Q

3) Axial Force “V”

28

At the base of each column the bending moment is . Horizontal shear is

and axial force is

“V” which is tensile in column “A” and compression in column “B”

Taking moments of external forces about “B” we get,

( ) ( ) ( )

However considering the equilibrium of O, A

Similarly

Hence from equation (1)

( )

(

)

If there are “n” columns in each row, we have

(

) and the shear in each column

The total stress in each column is that due to

1) Dead load of the structure and the contents

2) Axial force

3) Flexural stress due to “M” and

4) Shear stress due to shear “Q” which is considered to be negligibly small

(In the above case the wind load on the column faces has not been considered.)

4.3.2 Case2

Two rows of columns with horizontal braces. The below fig-11 shows a tank supported on two

columns (or two rows of columns) subjected to a horizontal wind load “P” on the exposed tank

surface. Here also again the wind load on exposed column faces has been neglected for

simplicity.

Two rows of columns have been connected with horizontal braces. It is assumed that the braces

are so stiff that the columns are constrained to maintain their axis vertical at their junctions

with braces.

29

It is also assumed that columns develop points of contra flexure there will be only horizontal

shear (=P/2, in the present case) and axial force, the bending moment being zero.

The bending moment at the junction of the column with the brace such as point “C” will be

given by.

Moment in the brace will be the sum of the two

( )

P I J

G h1 H o1

H E h2 F o2

O3

C h3 D MA - MB

A B V V

Fig.4.2. Staging subjected to wind

The moments at A and B evidently be

To find axial force “V” takes moments about “B”

30

( ) ( )

( )

(

)

If there are “n” columns in each row the above expressions are modified as follows.

(

*

4.3.3. Case 3

Frame work with three or more rows of columns

Below fig (12) shows the frame work with three rows of columns having “n” columns in each

row and stiffened with braces.

Let “P” be the total load due to wind on the exposed surface of the tank. Since the interior

columns “C” is braced on both sides and is held more stiffly than the exterior ones they are

assumed to take double horizontal shear than the exterior ones. Thus the horizontal shear at

the points contra flexure in each external column will be

while that in each middle column

will be

.

P

H

A MC C MB B

MA L/2 L/2

VA Vc VB=V

Fig.4.3. Wind force on three or more columns staging

31

If is the height of the lower panel

and

The whole frame work will rotate about the horizontal axis passing through “C”. Hence the

vertical (axial) force in “A’ and “B” will be equal, while the force in “C” will be zero.

(

)

4.3.4 Case 4

Circular group of columns

Below fig (4.4) shows the tower subjected to a wind force” on the water tank.

Let there are “n” columns arranged symmetrically on a circle of radius “r”. The other figure

shows the plan. The whole framework will have a tendency to rotate about the axis of bending

perpendicular to the direction of wind. Let Be the axial forces in the columns

situated at distances o, a, b,r. from bending axis. Due to wind moment “PH” at the column base

the axial loads are related as follows.

If the columns are assumed to be hinged at the bottom the external moment will be

equal to the moment of resistance

( ) ( ) ( )

For generalized treatment consider a staging having “n” number of columns and area of each

column is “A” subjected to the wind movement “Mw “. Therefore the columns are subjected to

the compression in addition to the gravity load. The additional compression on the columns

that is on the leeward side is proportional to the distance between the column and the axis of

bending. For simplification of the analysis let us replace the staging configuration with

equivalent ring of thickness “T”

32

Axis of bending

T

Wind Radius, R Radius (R)

Staging configuration Equivalent ring

Fig.4.4.Columns arranged symmetrically on a circle of radius “R”

“n” columns total area= nA

Thickness of equivalent ring= T=

Second moment of area of ring about its diameter =

Therefore bending stress

Where “R” is the Radius of column circle.

Therefore the force due to wind in leeward column=

Substituting the value of thickness “T”

(

)

For example number of columns are = 4, therefore

( )

4.4. Bracing

Horizontal bracings shall be provides if the height of the staging is more than 6m above the

foundation for connecting the columns rigidly by suitably spacing vertically at a spacing not

exceeding 6m.If the horizontal forces act in the critical direction bending moments in

horizontal braces shall be calculated. Therefore the final moments in braces shall be the sum of

in the lower and upper columns at the joint resolved in the direction of horizontal forces.

Two different supporting systems with basic supporting system

1) Radial bracing and

2) Cross bracing

33

Basic staging pattern staging with radial bracing staging with cross bracing

Fig.4.5. different patterns of the staging

4.5. Force in braces: Transverse shear

It is assumed that horizontal forces caused by the wind load is equally distributed on the top of

the columns, the force on each column is

. This force causes different effects in the horizontal

and diagonal braces thatare in horizontal braces compressive forces and in diagonal braces

tensile forces. They are specifying the two different cases of wind direction for 6-column

staging. Therefore by resolving the horizontal forces (

) in their planes the transverse shear in

each horizontal shear could be found. Therefore among the two cases the maximum shear

(=

) occurs in case (b), this is because the braces support the columns laterally

therefore an additional 2.5% of the column load is taken as shear in the panel. Thus total

transverse shear “Q” or the total horizontal force will be equal to +2.5% of (

)

34

Chapter 5

Joints

5.0. Introduction

Joints are potential sources of leakage therefore all the joint must be water tight. Design of

ordinary R.C.C structures is different from liquid retaining structures as the liquid retaining

structures requires that concrete should not crack and hence concrete should subject to the

tensile stresses which are within permissible limits. Therefore in various elements design of the

water tank particularly in the tank portion the stresses have to be checked whether they are

within the permissible limits or not.

A reinforced concrete member of liquid retaining structures is designed on the usual principles

ignoring tensile resistance of concrete in bending. Cracking may be caused due to restraint to

shrinkage expansion and contraction of concrete due to temperature or shrinkage and swelling

due to moisture effects. Such restraint may be caused by

1) The interaction between concrete and reinforcement during shrinkage due to drying

2) The boundary conditions

3) The differential conditions prevailing through the large thickness massive concrete.

Therefore the above said effects can be overcome by certain measures like use the smaller size

bars placed properly leads to closer cracks but of smaller width. Particularly the risk of cracking

due to temperature and shrinkage effects may be minimized by limiting the changes in

moisture content and temperature to which the structure as a whole is subjected. In case the

length of the structure is large it should be subdivided into suitable lengths separated by

movement joints. Especially where sections are changed the movement joints should be

provided.

Movement joints and Construction joints must be properly detailed using quality water stops.

Badly designed and detailed may permit flow of liquid and shall be avoided during design.

The special considerations required are as follows for reinforced concrete liquid retaining

structures.

i) The concrete should be durable, impervious and maintenance free. Durability

includes resistance to damage and protection against corrosion of reinforcements.

ii) In order to prevent leakage concrete leakage cracking in concrete shall be limited.

Concrete has numerous cracks. Large crack width permits leakage of liquids and shall

be restricted. Therefore two types of cracks shall be given attention.

35

a) Cracks due to shrinkage and temperature: These cracks are uniform throughout

the depth of concrete. Such cracks can be limited by resisting the shrinkage and

temperature forces by reinforcement.

b) Cracks due to applied loads: These cracks are wider on the surface and can

permit water which may corrode the reinforcement and finally may lead to

disintegration of concrete.

Surface cracks shall be limited to predetermined values as suggested by

respective codes of practice.

Is. 3370-2009 stipulates for liquid retaining structures the exposure as severe and permits crack

width up to 0.2 mm. This requirement necessitates limiting tensile stresses in concrete to

permissible value.

The design method developed considering limiting crack width is known as “no crack” design or

uncrack theory.

5.1. Common Joints in water tanks

The various types of joints may be categorized under 3 –heads.

1) Movement joints

2) Construction joints

3) Temporary open joints

5.1.1. Movement joints

These joints require special materials is to be incorporated in order to maintain water tightness

in accommodating relative moment between the sides of the joints. Therefore all movement

joints are essentially comes under flexible joints. Movement joints are of 3-types.

a) Contraction joints

b) Expansion joints

c) Sliding joints

5.1.1.1. Contraction joints

It is a type of typical movement joint which accommodates the contraction of the concrete.

The joint may be either a partial contraction joint in which there is discontinuity of concrete but

the reinforcement run through the joint or complete contraction joint in which there is

discontinuity of both concrete and steel. In both the cases no initial gap is kept at the joint but

only discontinuity is given during construction .In the former type the mouth of the joint is filled

36

with joint sealing compound and then strip painted while in the later type a water bar is

inserted. A water bar is a pre formed strip of impermeable material (such as a material,

polyvinyl chloride or rubber.)Joint sealing compounds are impermeable ductile materials which

are required to provide a water tight seal by adhesion to the concrete throughout the range of

joint movement.

5.1.1.2. Expansion joint

It is a movement joint with complete discontinuity in both reinforcement and concrete and is

intended to accommodate either contraction or expansion of the structure. In general such

joint requires the provision of an initial gap between the adjoining parts of a structure which by

closing or opening accommodates the expansion or contraction of the structure. The initial gap

is filled with joint filler. Joint fillers used are usually compressible sheet or strip materials used

spacers.

5.1.1.3. Sliding joint

Sliding joints is a type of movement joint with complete discontinuity in both concrete and

reinforcement at which special provision is made to facilitate relative movement in place of the

joint. A typical application of such joint is between floor and wall in some cylindrical tank

designs.

5.1.2. Construction joints

A construction joint is a type of joint in the concrete introduced for convenience in construction

at which special measures are taken to achieve subsequent continuity without provision for

further relative movement. It is therefore a rigid joint in contrast to a movement joint which is a

flexible joint.

Therefore the position and arrangement of all construction joints should be predetermined by

the engineer. Consideration should be given to limiting the number of such joints and to

keeping them free from possibility of percolation in a manner similar to contraction joints.

37

CHAPTER 6

COLUMN FOUNDATION

6.1. Introduction

The design of foundation and the forces on various elements of the tank because of wind loads

affected by the type of soil at foundation therefore Geotechnical investigation of the site is

sincerely required particularly the differential settlement effects should be properly taken into

account. At foundation level in order to determine the soil properties minimum 10 m deep

bore holes of 150 mm diameter shall be taken. If corrected “N” value (Standard penetration

Test) is less than 15, therefore the alteration is the ground shall be properly compacted to

achieve N> 15 and other measures shall be taken.

The selection of a particular type of foundation is often based on a number of factors. Such as

adequate depth to prevent frost damage, bearing capacity, settlement, quality, adequate

strength, adverse soil changes and wind forces. Based on the analysis of all the factors listed

above specific type of foundation would be recommended based on soil exploration by

engineer.

Separate footings may be provided for column staging and designed as per requirements of

EBCS-7, combined footing with or without tie beam or raft foundation in accordance with EBCS-

7 may be provided.

The foundation shall be so designed and proportioned that under both gravity loads of

tower(with tank full as well as empty) and effects due to horizontal forces the pressure caused

by these on the soil is within the safe bearing capacity and the footing in the critical direction

does not lift up at any point. Loss of contact between footing and underneath soil should not be

allowed .Loss of contact may be allowed in locations where the Safe bearing capacity is high

provided it is safe against overturning and such other considerations that are to be fulfilled.

Based on soil types in Ethiopia which are basically of expansive type mat foundations are very

much suitable. And also the wind load may act in any direction therefore it’s effect on the

foundation is not uniform in order to keep the stresses within the permissible limits and

distribute the loads to the lateral load (i.e., wind load) resisting system(staging) uniformly if the

foundation is of slab type which will act as a diaphragm. From economic considerations mat

foundations are often constructed because of the following reasons:

1) Large individual footings: It is in the case when the sum of individual footing areas

exceeds about one half of the total foundation area a mat foundation is often

constructed

38

2) Cavities or compressible lenses: when the subsurface exploration indicates that If there

will be unequal settlement caused by small cavities or compressible lenses below the

foundation a mat foundation can be used.

3) Shallow settlements: A mat foundation can be recommended when the mat foundation

would minimize differential settlements and shallow settlements predominate.

4) Unequal distribution of loads: In the case of some structures loads acting on different

areas of the foundation can have large difference in building loads. A mat foundation

would lend to distribute the unequal building loads and reduce the differential

settlements. Because the conventional spread footings could be subjected to excessive

differential settlement.

5) Hydrodynamic uplift: Due to a high groundwater table the foundation will be subjected

to hydrostatic uplift, In order to resist the uplift forces a mat foundation could be used

to resist

6.1. Problem statement: Analyze and design the Intze water tank form the wind load point

of view. The site is located in the urban center with a zero altitude. For different capacities

with varying staging height.

Solution: In order to differentiate how the wind load effect is varying with the variable

height of the staging. The sizes of the tanks are chosen 1200m3 and 1600m3 capacities. The

staging height is varying with 4m difference with 12m to 28m height. For analyzing the wind

load on the tank portion various provisions of the EBCS-1, wind load calculations are taken.

6.2. Wind data

Terrain category: Zone IV (according to the EBCE-1, Table 3.2 Terrain categories and related

parameters)

KT - Terrain factor =0.24, Zo (m) - roughness length = 1 and zmin(m)- Minimum height =16

Wind velocity: Basic mean reference wind velocity V O, ref= 22 m/sec.

Wind load calculation:

Pressure coefficients for the roof and bottom of the tank should be calculated. External

pressure coefficient is based on the exposure coefficient in this the variable is roughness

coefficient which depends upon the reference height. For the domes according to the EBCS-

1 A.2.8 given the reference height is equal to the “h+ f/2”. For finding the pressure

coefficients Fig. A.9 and A.10 should be used. For our case we are using the bottom is

circular therefore the fig A.10- External pressure coefficients Cpe10, for domes with circular

base should be used. The table is based on the h/d ratio and f/d ratio. For example the “f

39

“value is rise of the dome it is usually (1/5)th

of the diameter of the tank, therefore for 12 m

tank diameter the rise that is “f” is 2.4 meters. f/d ratio is 0.2 and h/d ratio for 24 meters

height staging with cylindrical walls height of the tank is 2/3 times the diameter of the tank.

Therefore for 9 m height cylindrical walls the ratio of h/d is 0.75, the |Cpe, 10 is “-1.1”.The

internal pressure cpi inside the tank may be because of any liquid stored or in the case of

water tanks if there is no pressure due to stored water inside the tank internal pressure will

be generated due to small permeability, may be because of openings provide (which may

small) at the roof level. Suppose if no openings exist, as in R.C.C water tanks CPi= 0

Usually roof pressure will be used with vertical loads for design of dome.

Therefore the overall horizontal Force on the Tank

On the top dome no horizontal force will act, because the load due to wind pressure on the

dome has been included in the net vertical force associated with an eccentricity.

For finding the force on circular cylinders external pressure coefficients are taken based on

the Reynolds number ( )

, and the external pressure coefficients Cpe of

circular cylinders are given by , and the external pressure coefficient

is given in fig A.22 for various Reynolds number as a function of angle and

the reference area Aref is = lb. Also the reference height is considered is equal to the height

above the ground of the section being considered. For conical bottom also to be considered

similarly. In the finding of the pressure on these elements average wind pressure

consideration should be taken. That is for that element top height considered and

calculated the roughness coefficient find the exposure coefficient and then finally the

reference wind pressure like this the bottom height should be taken and all the parameters

to find the reference wind pressure shall be calculated.

6.3. Staging

In order to calculate the wind force on columns, it is required to consider each column as

individual member and no shielding effect is considered on columns located on leeward

side as the columns are placed far apart on periphery only.

In designing the columns the load on the columns is due to container (with tank full), self-

weight of column and weight of the bracing. Therefore the weight on each of the column is

total load over number of columns in staging. Thus the following loading cases have to be

considered in the column design. And also bracing is used for increasing the stiffness of the

vertical members which resist the later load and also in order to reduce the bending and

40

shear in the columns. The design of the columns is done by using the limit state method.

Therefore the columns must be checked form the following loading cases.

i) D.L + L.L

ii) D.L + L.L +W.L , when tank is empty on wind ward column

iii) D.L + L.L +W.L , when tank is full on wind ward column

iv) D.L + L.L +W.L , when tank empty on Lee ward column

v) D.L + L.L +W.L , when tank full on Lee ward column

Wind action is represented either as a wind pressure or a wind force. The action on the

structure caused by the wind pressure is assumed to act normal to the surface except where

otherwise specified. e.g., for tangential friction forces.

Calculation of the pressure

External pressure:

The wind pressure acting on the external surfaces of a structure, we shall be obtained

from ( )

Internal pressure coefficient

Internal Pressure:

The wind pressure acting on the internal surfaces of structure ( )

Internal pressure coefficient

Net pressure:

The net wind pressure across a wall or an element is the difference of the pressures on each

surface taking due account of their signs (pressure directed towards the surface is taken as

positive and suction directed away from the surface as negative.

6.4. Wind forces from pressures

The wind forces acting on a structure or a structural component may be determined in two

ways

a) By means of global forces

b) As a summation of pressures acting on surfaces provided that the structure or the

structural component is not sensitive to dynamic response( )

41

The global force shall be obtained from the following expression:

( )

Force coefficient

Rreference area for (generally the projected area of the structure normal to the wind)

The following parameters are used several times are defined below:

Rreference mean wind velocity pressure derived from reference wind velocity. It is used

as the characteristic value

( ) Exposure coefficient accounting for the terrain and height above the ground “Z”. The

coefficient also modifies the mean pressure to a peak pressure allowing for turbulence

Z- Reference height appropriate for the relevant pressure coefficient (Z= )for external

pressure and force coefficient, (Z= ) for internal pressure coefficient.

For this case though it is cantilevered structure with a slenderness ratio

⁄ the

force is not to be calculated.

Reference wind

The reference mean wind velocity pressure shall be determined from

is the reference wind velocity

is air density

The air density is affected by altitude and depends on the temperature and pressure to be

expected in the region during wind storming. A temperature of has been selected as

appropriate for Ethiopia and the variation of mean atmospheric pressure with altitude is given

below.

42

Values of air density

Site altitude (m) above sea level

⁄

0 1.20

500 1.12

1000 1.06

1500 1.00

2000 0.94

Table 6.0. Value of Air density

Reference wind velocity

The reference wind velocity is defined as the “10” minute mean wind velocity at “10m”

above ground of terrain category-II having an annual probability of exceedence of

0.02(commonly referred to as having a mean return period of 50 years.

It shall be determined from

is the direction factor to be taken 1.0

is the temporary (seasonal) factor to be taken as 1.0

is the altitude factor as 1.0

is the basic value of the reference wind velocity to be taken as 22m/sec.

6.5. Roughness coefficient

The roughness coefficient ( ) accounts for the variability of the mean wind velocity at the

site of the structure due to

1) The height above ground level

2) The roughness of the terrain depending on the wind direction.

The roughness coefficient at height “Z” is defined by the logarithmic profile:

( ) (

*

( ) ( )

43

Tterrain factor

Rroughness length

Minimum height

Table 3.2 of EBCS-1 is providing terrain categories and related parameters.

6.6. Topography coefficient

The topography coefficient ( ) accounts for the increase of mean wind speed over isolated

hills and escarpments (not undulating and mountainous regions). It is related to the wind

velocity at the base of the hill or escarpment. It shall be considered for locations within

topography affected zone.

6.7. Exposure coefficient: For codification purposes it has been assumed that the quasi static

gust load is determined from

( ) ( ) ( )

( ) ( )

Terrain factor

( ) is the roughness coefficient

( ) is the topography coefficient

Wind load on various elements at 24 m height of staging for 1600m3 tanks

No

Description

Wind load in KN

Height from the ground

level

Moment at the base

1 Top Dome 16.48 38.0 626.24

2 Cylindrical wall 76.38 31.5 2405.97

3 Conical Dome 12.72 26.1 331.992

4 Columns 12 no’s 170.1 12 2041.2

5 Bracings 28.5 11.4 324.9

Total ∑ 304.18 Kn ∑ 5730.3 KN-m

Table6.1. Wind load on various elements

44

Details of the sizes of the of the members for 1200 m3 and 1600 m3 capacity tanks with a

staging height is 24m.

No Item description Tank 1200m3 Tank 1600m3

1 Top Dome 100 mm 130mm

2. Cylindrical wall 200 mm at top and 350 mm at bottom

200 mm at top and 450 mm at bottom

3. Top Ring beam 400 x 400 mm 500 x 500 mm

4. Middle ring beam 1200 x 600 1200 x 700 mm

5. Conical dome 550 mm 650 mm

6 Bottom dome 250 mm 330 mm

7. Bottom ring girder 600 x1200 700 x1200 mm

8 Column 700 mm 800 mm

9. Bracing 500 x 500 550 X 550 mm

10 Raft foundation. 600 mm thick slab 680 mm thick slab

Table 6.2.Sizes of the various members

For 24 m height staging the capacity of the tanks 1200m3 and 1600m3 reinforcement details

are shown below.

No Description Capacity 1200m3 Capacity 1600m3

1 Top dome Main and distribution

φ8 mm c/c 140mm both ways.

φ8 mm c/c 90 mm both circumferentially and meridionally

2 Top Ring beam B1 Main Stirrups

i) 12 φ16mm ii) φ 8mm two legged c/c 150 mm

i)16 φ16 mm ii) φ 8 mm two legged c/c 150 mm

3 Vertical wall

Main hoop steel- from top

i) 0 to 2m

ii)2 to 4m

iii) 4 to 9m

i) φ12mm c/c180 mm

on both sides.

ii) φ20 mm c/c250 mm

iii) φ25 mm c/c 150 mm

i) φ12 mmc/c 90 mm

both sides

ii) φ20 mm c/c 110 mm

iii) φ32 mm c/c100 mm

45

Distribution - From top

i) 0 to 2m

ii) 2 to 4m

iii) 4 to 9m

i) φ12 mmc/c 275 mm


iii) φ 12 mmc/c 110 mm

i) φ12mm c/c 190 mm


iii) φ 12 mm c/c 90 mm

4 Bottom ring beam B2

i) Main

ii) Stirrups

i) 24φ20 mm

ii) φ 10 mm c/c 100 mm

i) φ25 mm c/c 22 mm

ii) 12 mm c/c 100 mm

5 Conical wall

i) Main

ii) Distribution

i) φ25 mmc/c 150 mm


i) φ36 mm c/c100 mm


6 Bottom spherical dome

iii) φ12 mm c/c100 mm both sides

iii) φ16 mm c/c100 mm both sides

7 Bottom circular girder(B3)

i)Main top

ii) Main bottom

iii) Vertical stirrups

i) 16 φ25 mm

ii) 8 φ 25 mm

iii) φ 12 mm Six legged c/c

200 mm

i) 22 φ25 mm

ii)10 φ 25 mm

iii) φ 12 mm φ six legged

140 mm c/c

Supporting tower: Staging

1 Column

i) Main

ii) Lateral ties.

i) 10 φ 36 mm


i) 16 φ 36 mm

ii) φ 12 mm c/c220 mm

2 Bracing

i) Main

ii) Stirrups

i) 6 φ 25 mm at top and

bottom

ii) φ 12 mmc/c 250 mm

i) 8 φ 25 mm at top and

bottom


3 Circular girder for rafter

i)Top

ii)Bottom

iii)Stirrups

i) 6 φ 25 mm

ii) 10 φ 25 mm

iii) φ 12 mm c/c90 mm

i) 6 φ 36 mm

ii) 8 φ 36 mm

4 Raft foundation

i) Main

ii) Distribution

i) φ 25 mm c/c150 mm


i) φ 25 mm c/c120 mm


Table 6.3. Steel Requirement

46

Wind load variation with respect to the height wise variation of staging from 12m to 24 m

also variation of the capacity of the 1600 m3 tank.

Fig.6.1. (a) Wind pressure Vs Staging height

0

50

100

150

200

250

12m 16m 20m 24m

wind pressure

Height of staging

wind pressure Vs Staging height

6 columns

8 columns

12 columns

47

For 12 columns and the staging height is 24m the variation of wind force on the 1200m3 and

1600 m3 water tank.

Fig.6.2. (b) Variation of wind with respect to capacity

0

10

20

30

40

50

60

70

80

90

Top Dome Cylindrical wall Conical dome

Wind pressure

Elements in the tank

Variation of wind with respect to capcaity

For 1200m3

For 1600 m3

48

CHAPTER-7

EARTHQUAKE

7.0. Introduction

One of the major problems that may lead to failure of elevated concrete water tanks is

earthquake. Therefore the analysis of elevated tank must be carefully performed so that safety

can be assured when earthquake occurs and the tanks remain functional even after

earthquake. The irregular shape of the elevated water tanks for which most of the mass

concentrated in the upper part of the tank makes it more sensitive to any dynamic load

especially due to an earthquake. The elevated tanks are subjected to lateral and torsional

vibrations due to wind and seismic forces. These lateral forces physically induce two different

types of vibration in the water of the tank. Due to this vibration water exerts impulsive and

convective hydrodynamic pressure on the tank wall and tank base in addition to the hydrostatic

pressure. The effect of impulsive and convective hydrodynamic pressure should consider in the

analysis of tanks. For small capacity tanks, the impulsive pressure is always greater than the

convective pressure but it is vice versa for tanks with large capacity. Magnitudes of both the

pressure are different , A part of water at the upper portion of the tank participate in sloshing

motion (convective) with a longer period while the rest of the water at the bottom portion of

the tank experiences the same impulsive vibration as the tank container is rigidly attached with

container wall.

Basically there are three cases that are generally considered while analyze the elevated water

tank

1) Empty condition

2) Partially filled condition

3) Fully filled condition

For (1) and (3) case the tank will behave as a one mass structure and for (2) case the tank

behave as two mass structure. If we compared the case (1) and (3) with case (2) for maximum

EQ force the maximum force to which the partially filled tank is subjected may be less than

half the force to which the fully filled tank is subjected

Most elevated water tanks are never completely filled with water. Hence a two mass

idealization of the tank is more appropriate as compared to one mass idealization

Analysis and design of elevated water tanks against earthquake effect is of considerable

importance. This structure must remain functional even after an earthquake. Elevated water

tanks which typically consist of a large mass particularly susceptible to EQ damage. Thus

49

analysis and design of such structure against the EQ effect is of considerable importance. The

following points are to be considered at the time of seismic analysis of elevated water tanks.

1) Elevated water tanks are vulnerable to EQ excitation mainly because of the relatively

small resistance that the supporting system can offer during seismic events.

2) The seismic analysis and design of liquid storage tanks are complicated by many number

of problems for examples: Dynamic interaction between contained fluid and vessel

which is called fluid – structure interaction, sloshing motion of the contained fluid and

dynamic interaction between vessel and supporting structure. In addition the

supporting tower may need to be analyzed in post elastic state and for special cases a 3-

dimensional analysis may be required to take into torsional effect on the supporting

structure.

3) Tanks that are inadequately designed and detailed have suffered extensive damage

during past earthquake. Knowledge of pressures and forces acting on the walls and

bottom of containers during an earthquake and frequency properties of containers is

important for good analysis and design of EQ restraint structures/facilities.

A simplified analysis procedure has been suggested by Housner in 1963 for fixed base elevated

tanks. In this approach the two masses ( )

are assumed to be uncoupled and the EQ forces on the support are estimated by considering

two separate single degree of freedom systems. The mass represents only the sloshing of

the convective mass; the mass consists of the impulsive mass of the fluid the mass derived by

the weight of the container and by some parts self-weight of the supporting structure. This two

masses model suggested by Housner has been commonly used for seismic design of elevated

tanks. Similar equivalent masses and heights for this model based on the work of Velestos and

co-workers (Malhotra) with certain modification that the procedure simple are also suggested

in the Euro code-8(EC-8)

The total seismic response of a tank structure should be analyzed in terms of natural periods of

vibrations, base shear force and over turning moments. Periods are necessary after

determination of the two masses of with their locations and stiffness’s. Base shear

andoverturning moment for design can be estimated using standard structural dynamic

procedures. It should be noted that concrete and steel tanks show different behavior under a

seismic action. In the case of concrete tanks the wall may be taken as rigid whereas in the case

of steel tanks the wall may be taken as flexible.

Parameters of spring mass model (i.e.

) are available for circular and

rectangular tanks only. For tanks other shapes equivalent circular tank is to be considered Joshi

(2000) has shown that such an approach gives satisfactory results for Intze tanks. Euro code-8

has suggested equivalent circular tank approach. And for tank shapes other than circular and

50

rectangular (like Intze and truncated conical shape ) the value of

shall correspond to that of

an equivalent circular tank of same volume and diameter equal to diameter of tank at top level

of liquid and

of equivalent circular tank shall be used.

A) The natural period of the impulsive mode of vibration in second for elevated tank is

√

where,

Mass of container and 1/3 mass of staging

Impulsive mass (The impulsive and convective masses are given in Table B.1

as fractions of the total liquid mass “m”

Lateral stiffness of staging

Lateral stiffness of the staging ( ) is the horizontal force required to be applied at the Centre

of gravity of the tank to cause a corresponding unit horizontal displacement. The flexibility of

bracing beam shall be considered in calculating the lateral stiffness of elevated moment

resisting frame type tank staging. For elevated tanks with moment resisting type frame staging

the lateral stiffness can be evaluated by computer analysis or by simple procedures (Sameer

and Jain 1992) or by established structural analysis method.

Lateral stiffness of staging is defined as the force required to be applied at the C.G of tank so as

to get a corresponding unit deflection. C.G of the tank is the combined C.G of empty container

and impulsive mass. However in this example C.G of tank is taken as C.G of empty container.

Natural periods given by EC-8 for impulsive mode √

√ √

Mass density of the liquid

Young’s modules of elasticity of tank material

The coefficients ) are obtained from Table B.1

Equivalent uniform thickness of the tank wall

For tanks with non-uniform wall thickness “S” may be computed by taking a weighted

average over the wetted height of the tank wall, assigning highest weight to the thickness near

the base of tank where the strain is maximum.

B) The natural period of the convective mode vibration in seconds √ where R-

in meters.

51

From Table B.1 of Ec-8 part-4.

C) Total base shear at the bottom of staging is given √

D) Total over turning moment at base of staging is given √

For elevated tank staging components should be designed for the critical direction of seismic

force .Different components of staging may have different critical directions. For elevated tanks

supported on frame type staging the design of the staging member should be for the most

critical direction of horizontal base acceleration. For a staging consisting of four columns

horizontal acceleration in diagonal direction (i.e. ) turns out to be most

critical for axial force in columns. For brace beam most critical direction of loading is along the

length of the brace beam. Sameer and Jain (1994) have discussed in detail the critical direction

of horizontal base acceleration for frame type staging.

Problem: Analysis and Design of Elevated Intze water tank from the seismic forces.

Solution : for this problem the dimensions that were derived in the wind analysis for the Intze

elevated tank of size 1600 m3 capacity with a staging height of 28 m , the diameter of the

cylindrical wall is 12m and the height of the tank is 9m and the tank is filled with water to a

height of 8m. The walls of the cylindrical portion of the tank are of varying thickness having

four courses, each 2.25 m high. The lower most course is 450 mm thick and the next to that is

350 mm and the top most course is having 200 mm and below the top course the thickness is

250mm.The dimensions of the 1600 m3 capacity and 28 m staging height Intze tank from the

wind analysis is

Element Type Dimension

Top Dome 130 mm

Top Ring beam 500X500 mm

Cylindrical wall 200 mm @ top and 450 mm @ bottom

Bottom Ring beam 1200 X 700 mm

Circular Ring beam 1200 X 700 mm

Bottom Dome 330 mm

Conical Dome 650 mm

Braces 550X550 mm

Columns Circular 800 mm dia.

Table7.0. Dimensions of the tank from the wind analysis

52

2.4m

9m

12m

2.25m

1.5m

7.5m

Fig.7.0. Dimensions of the various members

53

Weight Calculation:

Components Calculation Weight (KN)

Top Dome (130mm)

=

[ (

(

)

⁄ )

⁄

]

=

= 454.68

Top Ring beam ( )( ) =245.5

Cylindrical wall (

(

))

( )

=2832

Bottom ring beam ( )( ) = 871

Circular ring beam ( ) ( ) =574

Conical dome

[(

) ( )

]

=474.34

Bottom spherical dome

(

[

( )

⁄ ]

⁄

)

=536.84

Columns ( ) (

)

⁄

=4171

Braces ( ) =668.47

Weight of the water *

( )

(

( )

( )+

=1137x103 Kg

Table 7.1.Weight of the elements of the tank

54

7.1. Height of the C.G of empty container above top of circular ring beam:

C.G of the empty container consists of: Top dome, top ring beam, cylindrical wall, bottom ring

beam, bottom dome and circular ring beam.

* (

) (

) (

) (

) (

) (

) +

⁄

= 5.769m

Therefore the height of the empty container from top of footing =

m

Weight of the empty container = 454.68+245.5+2832.2+871+574+474.34+536.84= 5988 KN

Weight of staging = 4171+668.47= 4839.47 KN

Hence weight of the empty container +one third of the weight of the staging =

Model properties: First the equivalent uniform thickness of the tank wall is calculated by the

weighted average method using weights equal to the distance from the liquid surface.

(

) (

) (

)

Therefore S= 0.3779m

For concrete E=

For obtaining parameters of spring mass model, an equivalent circular container of same volume and

diameter equal to diameter of tank at top level of liquid will be considered. Let H1 be the height of

equivalent circular cylinder

( ) Therefore H1= 10m

For

for This value from the table B.1

55

1.66.7 6.0975 1.48 0.7053 0.295 0.441 0.705 0.541 0.7415

Table 7.2. H/R ratio

Now calculate the Time period for impulsive and convective

√

√ √

√

√

√

0.0137 s

√ √ 3.62 s

Hence

801X103 kg

335.415X103 Kg

4.41 m

7.2. Seismic responses:

The impulsive spectral acceleration for obtain for 5% damped elastic response

spectrum. The convective spectral acceleration for obtain for the 0.5% damped

response spectrum .This is based on the ANNEX B (IINFORMATIVE) SEISMIC ANALYSIS

PROCEDURES FOR TANKS. This Annex provides information on seismic analysis procedures for

tanks subjected to horizontal and vertical excitation and having the following characteristics: a)

cylindrical shape, with vertical axis and circular or rectangular cross-section; b) rigid or flexible

foundation; c) fully or partially anchored to the foundation. ( ) The impulsive spectral

acceleration obtained from a 2% damped elastic response spectra for steel or pre stressed

concrete and a 5% damped elastic response spectrum for concrete tanks, ( ) Convective

spectral acceleration obtained from a 0.5% damped elastic response spectrum.

For finding ( ) and ( ) according to the EBCS-8 which has given formulas based on the 5%

damping curve for the elastic response spectrum, therefore application of damping correction

56

factor to it is inevitable. The value of the damping correction factor “ may be determined by

the expression according to the new draft of the EBCS-8

√

is the damping factor with reference value for 5% viscous damping.

is the viscous damping ratio of the structure expressed as percentage. Therefore for the

0.5% damping the correction factor is √

The structure is located on the Ground type is “B” according to the EBCS-8 ,Table 3.1 Ground

types, the site soil satisfies as deposits of very dense sand, gravel or very stiff at least several

tens of meters in thickness characterized by a gradual increase of mechanical property with

depth. Therefore Table 3.2 values of the parameters describe the recommended Type-1 elastic

response spectra to be used. From this table for type “B” soil the corresponding parameters are

( ) ( ) ( )

Table 7.3. Type-1 spectrum for “B” class soil

For finding horizontal response spectrum:

The EBCS-8 is providing formula for finding the horizontal components of the seismic action the

elastic response spectrum is defined by the expressions given in the clause 3.2.2.2. For time

periods for the impulsive and convective are , for these values

the horizontal response spectrum values are

For impulsive time period , i.e, it satisfying the condition ,(

) the equation for finding the horizontal elastic response spectrum is

( ) [

( )]

Similarly for the convective time period ie, it is satisfying the relation

( ) the equation for finding the horizontal elastic response

spectrum is

( ) (

)

57

7.3. Fundamental requirement according to the EBCS-8:

The structure shall be designed and constructed to withstand the design seismic action without

local or global collapse thus retaining its structural integrity and a residual load bearing capacity

after the seismic events. The design seismic action is expressed in terms of a) The reference

seismic action associated with a reference probability of exceedence in 50 years or a

reference return period and b) the importance factor to take into account reliability

differentiation. The values to be ascribed to for or is in the National Annex

document. The recommended values are Therefore the

importance factors given in EBCS code are related to the building structures. For the tanks the

importance factor has taken from the EC-8, it has given based on the reliability, the classes

defined according to this are three defined corresponding to situations with high (Class-1),

medium (Class-2) and low(Class-3). Depending on the tank contents an importance factor is

assigned to each of the three classes.

Importance factor ( ) for tanks according to EC-8.

Tank contents

Importance factor ( )

Class-1 Class-2 Class-3

Drinking water, non-toxic, nonflammable chemicals

1.2 1.0 0.8

Firefighting water, non-volatile toxic chemicals lowly flammable petrochemicals.

1.4 1.2 1.0

Volatile toxic chemicals, explosive and higher flammable liquids

1.6 1.4 1.2

Table 7.4. Importance factor for tanks

7.4. Seismic zones: Clause 3.2 of EBCS-8

National territories shall be subdivided into seismic zones depending on its local hazard. By

definition the hazard within each zone is assumed to be constant. For most of the applications

of EBCS-8 the hazard is described in terms of single parameter i.e., the value of the reference

peak ground acceleration on type “A” ground . The reference peak ground acceleration on

type “A” ground for use is derived from zonation maps found in the National Annex. The

reference peak ground acceleration chosen for each seismic zone corresponds to the reference

return period of the seismic action for the no collapse requirement (or reference

probability of exceedence in 50 years ). An importance factor equal to 1.0 is assigned to

this reference return period. For return periods other than the reference the design ground

acceleration on type “A” ground is equal to times importance factor.( ).

58

Therefore in the analysis according to the EC-8 elastic spectrum (Type-1, Soil type –B) was used

as well as: reference peak ground acceleration importance factor for the

structural class -3 , which gives design ground acceleration .

Calculate the Horizontal response spectrum for the impulsive time period is

( ) *

( )+ 5.242

Similarly for the Convective time period the horizontal response spectrum is

( ) *

+ 0.6575

According to the EBCS-8

Fb = Sd (T1) m λ

Where,

Sd (T1) is the ordinate of the design spectrum at period T1;

T1 is the fundamental period of vibration of the building for lateral motion in the direction

considered;

λ is the correction factor, the value of which is equal to: λ= 0.85 if T1 < 2 TC and the building has

more than two story’s, or λ = 1.0 otherwise

Therefore base shear at the bottom of the staging in impulsive mode is:

( )( ) , the value of the for the condition 0.0137< 2(0.25) is equal to 0.85

( ) 6955.79X103 kg

Similarly the base shear in the convective mode,

The λ is the correction factor for the condition 3.62 <2(0.25) is not satisfying therefore the

correction factor λ= 1

( )*1=220X103 Kg

Total shear at the bottom of the staging =69557+2200 =71757 KN

Moment at the bottom:

Overturning moment at the base of the staging in impulsive mode

( )( ( ) )

( (5.41+28.35) +760X 34.119) = 27768x103 kg-m=277.6 MNm

Similarly the overturning moment in convective mode is

59

( )( ( )

( ( )) 7886 X103 kg-m=78.86 MNm

Total over turning moment = 277.6 + 78.86 =356.46 MNm

Comparison of the base shear and overturning moment for wind load and Earth quake load

Fig.7.1. Base shear comparison for wind and earthquake

0

10000

20000

30000

40000

50000

60000

70000

80000

base shear

wind load KN

Earth quake load KN

60

Comparison of the over turning moments for wind and earth quake load

Fig.7.2 overturning moment comparison for wind and earthquake.

0

50000

100000

150000

200000

250000

300000

350000

400000

over turning moment

wind kn-m

earth quake kn-m

61

Chapter 8

Modeling 8.0 Introduction The modeling water tanker is made in SAP2000 V18 Software. In the modeling all shell elements are

modeled as a thin shell element with appropriate stiffness modifier. For the beams and columns

stiffness modifier according to ACI code have been used.

The loading is defined in load Pattern definition dialog box of SAP2000. For the definition of wind load,

EURO code-1 2004 has been used with appropriate side coefficients. Earthquake load is defined using

response spectrum load case. After defining all load cases and patterns, the loads are combined

following the EBCS (Ethiopian Building Codes of Standard) rules of combination.

Definition of material properties, frame sections and areal elements has been performed. Then the

modeling (drawing of each element) is done. Then load is applied to the corresponding elements.

Analysis and design of the shells, beams and columns are also performed in SAP2000 program.

8.1 Material definition Two materials are used in water tanker design. Concrete with a grade of 25MPa and Reinforcement of

grade S-400.

Fig.8.1.Concerte material definition

62

Fig.8.2. Reinforcement bar definition

For the definition of reinforcement bar property rigid plastic stress vs strain is assumed which is curve B

in the figure below.

63

Fig.8.3.Idealized rebar stress-strain profile

8.2 Frame section definition

There are three beams in the water tanker. The first one is the top ring beam located at intersection of

top dome and the cylinder which have a dimension of 500mm by 500mm, in SAP2000 it is labeled as

B1.The second one is the circular ring beam located at intersection of the cylinder and conical dome

which have a dimension of 1200mm by 700mm, in SAP2000 it is labeled as B2.The third one is the

circular ring beam located at intersection of the bottom dome and columns which have a dimension of

1200mm by 700mm, in SAP2000 it is labeled as B3. All twelve columns are circular and have a dimension

of diameter 800mm.

64

Fig.8.4.Beam definition

Fig.8.5. Stiffness modifier

Fig.8.6. Column definition

Fig.8.7. Stiffness modifier

The other two beams (B-2 and B-3) are also defined with similar fashion as in B-1 definition.

65

8.3 Area element definition A total of four shells are used in the water tanker modeling and analysis. This is top dome used as roof

system, cylindrical wall, conical dome and bottom dome. The top dome has a diameter of 12m and

thickness of 130mm. The cylindrical has a diameter of 12m with thickness varying from 200mm at the

top to 450mm at the bottom where the height of the cylinder is 9m. The conical dome has a thickness of

650 mm. The bottom dome has a diameter of 7.5m and thickness of 330mm.

Fig.8.8. Area element definition in SAP2000

Fig.8.9. Stiffness modifiers

66

8.4 Load and combination definition A total of nine load patterns are defined and there are ten load cases including response spectrum for

earthquake. The total number of load combination is eight.

TABLE: Load Pattern Definitions

Load Pattern Design Type Self-Weight Multiplier

Text Text Unit less

Self-Weight DEAD 1

Super Dead SUPER DEAD 0

Water Full SUPER DEAD 0

Water Half SUPER DEAD 0

Lateral Pressure Full SUPER DEAD 0

Lateral Pressure Half SUPER DEAD 0

Sloshing SUPER DEAD 0

Live Roof ROOF LIVE 0

WIND WIND 0

Table 8.1. Load pattern definition

TABLE: Load Case Definitions

Case Type Design Type Des Act Opt Design Action

Text Text Text Text Text

Self-Weight LinStatic DEAD ProgDet Non-Composite

Super Dead LinStatic SUPER DEAD ProgDet Long-Term Composite

Water Full LinStatic SUPER DEAD ProgDet Long-Term Composite

Water Half LinStatic SUPER DEAD ProgDet Long-Term Composite

Lateral Pressure Full LinStatic SUPER DEAD ProgDet Long-Term Composite

Lateral Pressure Half LinStatic SUPER DEAD ProgDet Long-Term Composite

Sloshing LinStatic SUPER DEAD ProgDet Long-Term Composite

Live Roof LinStatic ROOF LIVE ProgDet Short-Term Composite

WIND LinStatic WIND ProgDet Short-Term Composite

MODAL LinModal OTHER ProgDet Other

RSA LinRespSpec QUAKE ProgDet Short-Term Composite

Table 8.2. Load case definition

Super dead load accounts to the additional load coming from cement screed and plastering and other

dead loads.

Response spectrum is defined based on Eurocode-1998.

67

Fig.8.10 Response spectrum function definition

Fig.8.11 Load combinations

The sloshing effect is considered when the water in the tanker is half. Sloshing effect has positive effect

on the performance of the structure during earthquake. But to see whether this is correct or not it has

been included in the analysis.

68

For the wind load combination when the water in the tanker is empty will be the governing combination

but for completeness when the water is full wind load is applied.

8.5 Modeling The step by step modeling of the water tanker follows the following procedures:

First columns are modeled then the beams (bracing beams) are drawn.

Then bottom are modeled

Ring beam three is modeled then the cylinder shell is modeled

Top ring mean is modeled

Finally, the top dome is modeled

Fig.8.12. Column and bracing beam model

69

Fig.8.13.Conical dome

Fig.8.14.Bottom dome

70

Fig.8.15. Cylindrical shell

Fig.8.16. Top Dome

71

Chapter 9 Analysis Result

9.0 Introduction

For the analysis of elevated water tanker linear elastic analysis method has been used. After all loadings

are applied to the corresponding elements analysis is carried out. First standard solver is used to check

whether a warning or error message has been generated. The analysis was full scale three-dimensional

analysis which has all six degree of freedom.

SAP2000 v18.1.1 Ultimate 64-bit (Analysis Build 9447/64)

File: D:\Projects\Water Tanker\SAP2000 Model\model-1-15.LOG

B E G I N A N A L Y S I S

2016/07/13 17:14:30

RUNNING ANALYSIS AS A SEPARATE PROCESS

USING THE STANDARD SOLVER (PROVIDES COMPLETE INSTABILITY INFORMATION)

NUMBER OF JOINTS = 5707

WITH RESTRAINTS = 12

NUMBER OF FRAME/CABLE/TENDON ELEMENTS = 528

NUMBER OF SHELL ELEMENTS = 5760

NUMBER OF CONSTRAINTS/WELDS = 49

NUMBER OF LOAD PATTERNS = 9

NUMBER OF ACCELERATION LOADS = 9

NUMBER OF LOAD CASES = 11

E L E M E N T F O R M A T I O N

17:14:30

L I N E A R E Q U A T I O N S O L U T I O N

17:14:31

FORMING STIFFNESS AT ZERO (UNSTRESSED) INITIAL CONDITIONS

TOTAL NUMBER OF EQUILIBRIUM EQUATIONS = 34170

APPROXIMATE "EFFECTIVE" BAND WIDTH = 695

NUMBER OF EQUATION STORAGE BLOCKS = 1

MAXIMUM BLOCK SIZE (8-BYTE TERMS) = 23522799

SIZE OF STIFFNESS FILE(S) = 179.595 MB

72

NUMBER OF EQUATIONS TO SOLVE = 34170

---------------------------------

BASIC STABILITY CHECK FOR LINEAR LOAD CASES:

NUMBER OF NEGATIVE STIFFNESS EIGENVALUES SHOULD BE ZERO FOR

STABILITY.

(NOTE: FURTHER CHECKS SHOULD BE CONSIDERED AS DEEMED NECESSARY,

SUCH AS REVIEWING EIGEN MODES FOR MECHANISMS AND RIGID-BODY

MOTION)

NUMBER OF NEGATIVE EIGENVALUES = 0, OK.

---------------------------------

L I N E A R S T A T I C C A S E S

17:14:46

USING STIFFNESS AT ZERO (UNSTRESSED) INITIAL CONDITIONS

TOTAL NUMBER OF CASES TO SOLVE = 9

NUMBER OF CASES TO SOLVE PER BLOCK = 9

LINEAR STATIC CASES TO BE SOLVED:

CASE: SELF WEIGHT

CASE: SUPER DEAD

CASE: WATET FULL

CASE: WATET HALF

CASE: LATERAL PRESSURE FULL

CASE: LATERAL PRESSURE HALF

CASE: SLOSHING

CASE: LIVE ROOF

CASE: WIND

E I G E N M O D A L A N A L Y S I S

17:14:46

CASE: MODAL

USING STIFFNESS AT ZERO (UNSTRESSED) INITIAL CONDITIONS

NUMBER OF STIFFNESS DEGREES OF FREEDOM = 34170

NUMBER OF MASS DEGREES OF FREEDOM = 17085

MAXIMUM NUMBER OF EIGEN MODES SOUGHT = 12

MINIMUM NUMBER OF EIGEN MODES SOUGHT = 1

NUMBER OF RESIDUAL-MASS MODES SOUGHT = 0

NUMBER OF SUBSPACE VECTORS USED = 24

73

RELATIVE CONVERGENCE TOLERANCE = 1.00E-09

FREQUENCY SHIFT (CENTER) (CYC/TIME) = .000000

FREQUENCY CUTOFF (RADIUS) (CYC/TIME) = -INFINITY-

ALLOW AUTOMATIC FREQUENCY SHIFTING = YES

Original stiffness at shift: EV= 0.0000000E+00, f= .000000, T= -

INFINITY-

Number of eigenvalues below shift = 0

Found mode 1 of 12: EV= 7.1051740E+00, f= 0.424236, T=

2.357179


2.357179


1.874753


0.320345


0.320345


0.228668


0.228668


0.205349


0.129743


0.129216


0.129216


0.101416

NUMBER OF EIGEN MODES FOUND = 12

NUMBER OF ITERATIONS PERFORMED = 11

NUMBER OF STIFFNESS SHIFTS = 0

R E S P O N S E - S P E C T R U M A N A L Y S I S

17:14:53

CASE: RSA

TYPE OF EXCITATION = STANDARD GROUND

ACCELERATION

USING MODES FROM CASE: MODAL

NUMBER OF DYNAMIC MODES TO BE USED = 12

A N A L Y S I S C O M P L E T E

2016/07/13 17:14:53

As can been seen from the above text taken from SAP2000 the is no warning or error messagereported.

After this verification standard solver is changed to advanced solver.

74

9.1 Labeling of elements

The columns are divided in to five parts along its height, since columns with height above five to eight

(5-8) meters generally will be very slender depending on the size of beam and column as well as the

supporting condition. For this elevated water tanker, the bottom column height is 5.75m and the rest

columns are 5m in length. This is made possible by providing diagonal bracing of the columns. All

columns are reinforced concrete frames having a circular shape and diameter of 800mm.

Fig.9.1. Column label

75

Fig.9.2. Bracing beam @5.75m


Fig.9.4.Bracing beam @15.75m


Fig.9.6.Bracing beam @25.75m

76

9.2 Results 9.2.1 Beam and Column forces

TABLE: Element Forces - Frames

Frame Station Output Case Case Type Step Type P V2 V3 M2 M3

Text m Text Text Text KN KN KN KN-m KN-m

1 0 DL+LL Full Combination

-239.224 -30.469 -2.318E-08 -7.189E-08 -43.031

1 0.46875 DL+LL Full Combination

-239.224 -26.66 -2.318E-08 -6.102E-08 -29.6414


-239.224 -22.852 -2.318E-08 -5.016E-08 -18.0371


-239.224 -19.043 -2.318E-08 -3.929E-08 -8.2181


-239.224 -15.234 -2.318E-08 -2.843E-08 -0.1843


-239.224 -11.426 -2.318E-08 -1.756E-08 6.0642


-239.224 -7.617 -2.318E-08 -6.694E-09 10.5274


-239.224 -3.809 -2.318E-08 4.171E-09 13.2053


-239.224 -5.24E-08 -2.318E-08 1.504E-08 14.0979

1 0 DL+LL Half Combination

-227.35 -30.469 -1.429E-08 -4.671E-08 -41.927

1 0.46875 DL+LL Half Combination

-227.35 -26.66 -1.429E-08 -4.001E-08 -28.5374


-227.35 -22.852 -1.429E-08 -3.332E-08 -16.9331


-227.35 -19.043 -1.429E-08 -2.662E-08 -7.1141


-227.35 -15.234 -1.429E-08 -1.992E-08 0.9196


-227.35 -11.426 -1.429E-08 -1.323E-08 7.1681


-227.35 -7.617 -1.429E-08 -6.53E-09 11.6313


-227.35 -3.809 -1.429E-08 1.671E-10 14.3092


-227.35 -7.574E-08 -1.429E-08 6.864E-09 15.2019

1 0 DL+LL+WIND Full Combination

-305.796 -22.674 0.046 0.1162 -20.1071

1 0.46875 DL+LL+WIND Full Combination

-305.796 -18.866 0.046 0.0948 -10.3711


-305.796 -15.057 0.046 0.0734 -2.4205


-305.796 -11.249 0.046 0.0521 3.7449


-305.796 -7.44 0.046 0.0307 8.125


-305.796 -3.631 0.046 0.0093 10.7199


-305.796 0.177 0.046 -0.0121 11.5294


-305.796 3.986 0.046 -0.0334 10.5537


-305.796 7.794 0.046 -0.0548 7.7927

1 0 DL+WIND Full Combination

-316.284 -21.231 0.054 0.1377 -15.8401

1 0.46875 DL+WIND Full Combination

-316.284 -17.422 0.054 0.1124 -6.7807


-316.284 -13.614 0.054 0.087 0.4933


-316.284 -9.805 0.054 0.0617 5.9821


-316.284 -5.997 0.054 0.0364 9.6856


-316.284 -2.188 0.054 0.011 11.6039


-316.284 1.621 0.054 -0.0143 11.7368


-316.284 5.429 0.054 -0.0396 10.0845

77


-316.284 9.238 0.054 -0.065 6.6469

1 0 DL+LL+WIND Empty Combination

-283.48 -22.674 0.046 0.1162 -17.8414

1 0.46875 DL+LL+WIND Empty Combination

-283.48 -18.866 0.046 0.0948 -8.1054


-283.48 -15.057 0.046 0.0734 -0.1548


-283.48 -11.249 0.046 0.0521 6.0106


-283.48 -7.44 0.046 0.0307 10.3907


-283.48 -3.631 0.046 0.0093 12.9856


-283.48 0.177 0.046 -0.0121 13.7951


-283.48 3.986 0.046 -0.0334 12.8194


-283.48 7.794 0.046 -0.0548 10.0584

1 0 DL+WIND Empty Combination

-293.968 -21.231 0.054 0.1377 -13.5744

1 0.46875 DL+WIND Empty Combination

-293.968 -17.422 0.054 0.1124 -4.515


-293.968 -13.614 0.054 0.087 2.759


-293.968 -9.805 0.054 0.0617 8.2478


-293.968 -5.997 0.054 0.0364 11.9513


-293.968 -2.188 0.054 0.011 13.8696


-293.968 1.621 0.054 -0.0143 14.0025


-293.968 5.429 0.054 -0.0396 12.3502


-293.968 9.238 0.054 -0.065 8.9126

1 0 EQ Full Combination Max -178.577 -18.078 0.144 0.101 -18.1746

1 0.46875 EQ Full Combination Max -178.577 -15.222 0.144 0.0414 -10.3699

1 0.9375 EQ Full Combination Max -178.577 -12.365 0.144 0.048 -3.9042

1 1.40625 EQ Full Combination Max -178.577 -9.509 0.144 0.1094 1.2226




1 3.28125 EQ Full Combination Max -178.577 1.917 0.144 0.376 11.4694


1 0 EQ Full Combination Min -180.259 -27.625 -0.144 -0.101 -46.3719

1 0.46875 EQ Full Combination Min -180.259 -24.769 -0.144 -0.0414 -34.0922




1 2.34375 EQ Full Combination Min -180.259 -13.343 -0.144 -0.2419 1.6366

78




1 0 EQ Half Combination Max -171.54 -33.552 0.144 0.101 -63.2285

1 0.46875 EQ Half Combination Max -171.54 -30.695 0.144 0.0414 -48.1706





1 2.8125 EQ Half Combination Max -171.54 -16.413 0.144 0.3089 7.037



1 0 EQ Half Combination Min -173.223 -43.098 -0.144 -0.101 -91.4258

1 0.46875 EQ Half Combination Min -173.223 -40.242 -0.144 -0.0414 -71.8929





1 2.8125 EQ Half Combination Min -173.223 -25.96 -0.144 -0.3089 5.6846



Table 9.1. Bracing beam forces for label-1

TABLE: Element Forces - Frames

Frame Station Output Case Case Type StepType P V2 V3 M2 M3

Text m Text Text Text KN KN KN KN-m KN-m


-2883.95 5.137E-11 -3.869 -3.765 3.992E-08


-2930.916 5.137E-11 -3.869 7.3594 3.977E-08


-2236.847 -8.517E-10 -3.887 -14.9581 1.973E-08


-2283.814 -8.517E-10 -3.887 -3.7831 2.218E-08


-2330.781 -8.517E-10 -3.887 7.3919 2.463E-08


-2836.94 -111.803 -3.867 -14.8805 -184.8246


-2883.907 -111.803 -3.867 -3.7628 136.6104


-2930.873 -111.803 -3.867 7.3548 458.0453

79


-2829.829 -132.508 -3.867 -14.8806 -219.0514


-2876.795 -132.508 -3.867 -3.7629 161.9086


-2923.762 -132.508 -3.867 7.3548 542.8685


-1636.669 -111.803 -3.903 -15.0209 -184.8246


-1683.636 -111.803 -3.903 -3.7998 136.6104


-1730.603 -111.803 -3.903 7.4213 458.0453


-1629.558 -132.508 -3.903 -15.021 -219.0514


-1676.524 -132.508 -3.903 -3.7999 161.9086


-1723.491 -132.508 -3.903 7.4213 542.8685

475 0 EQ Full Combination Max -1514.657 72.853 36.692 9.3921 123.955






475 0 EQ Half Combination Max -1064.555 264.352 36.679 9.3409 437.6662

475 2.875 EQ Half Combination Max -1099.78 264.352 36.679 91.0317 -150.5881


475 0 EQ Half Combination Min -2290.716 118.646 -42.51 -31.7774 189.7563

475 2.875 EQ Half Combination Min -2325.941 118.646 -42.51 -96.7062 -323.1077



-2836.983 -1.935 -3.351 -12.8946 -7.4447


-2883.95 -1.935 -3.351 -3.2606 -1.8825


-2930.916 -1.935 -3.351 6.3734 3.6797


-2236.847 -1.943 -3.366 -12.9541 -7.479


-2283.814 -1.943 -3.366 -3.2763 -1.8915


-2330.781 -1.943 -3.366 6.4016 3.6959


-3430.569 -103.907 13.681 52.5146 -154.5131


-3477.535 -103.907 13.681 13.1829 144.2196


-3524.502 -103.907 13.681 -26.1488 442.9524


-3533.389 -122.791 16.834 64.6259 -181.7489

80


-3580.355 -122.791 16.834 16.2276 171.2753


-3627.322 -122.791 16.834 -32.1707 524.2996


-2230.298 -103.925 13.649 52.393 -154.5834


-2277.264 -103.925 13.649 13.1509 144.2011


-2324.231 -103.925 13.649 -26.0913 442.9856


-2333.118 -122.809 16.803 64.5043 -181.8192


-2380.085 -122.809 16.803 16.1956 171.2568


-2427.051 -122.809 16.803 -32.1132 524.3328







477 0 EQ Half Combination Max 60.973 243.412 17.964 -54.6288 359.8082

477 2.875 EQ Half Combination Max 25.748 243.412 17.964 55.055 -164.883






-2836.983 -3.351 -1.935 -7.4447 -12.8946


-2883.95 -3.351 -1.935 -1.8825 -3.2606


-2930.916 -3.351 -1.935 3.6797 6.3734


-2236.847 -3.366 -1.943 -7.479 -12.9541


-2283.814 -3.366 -1.943 -1.8915 -3.2763


-2330.781 -3.366 -1.943 3.6959 6.4016


-3865.191 -85.658 15.096 57.9615 -84.4374


-3912.158 -85.658 15.096 14.5602 161.8283


-3959.125 -85.658 15.096 -28.841 408.094


-4048.497 -100.9 18.25 70.0729 -97.6877


-4095.464 -100.9 18.25 17.605 192.3999

81


-4142.431 -100.9 18.25 -34.8629 482.4875


-2664.92 -85.689 15.078 57.8913 -84.5591


-2711.887 -85.689 15.078 14.5417 161.7963


-2758.854 -85.689 15.078 -28.8078 408.1516


-2848.226 -100.931 18.232 70.0026 -97.8093


-2895.193 -100.931 18.232 17.5865 192.3679


-2942.16 -100.931 18.232 -34.8297 482.545







479 0 EQ Half Combination Max 1006.208 196.223 29.462 -14.5821 181.8556






Table 9.2. Column Forces for label 475,477 and 479

82

9.2.2. Deformed shapes

Fig.9.7. Un-deformed shape

Fig.9.8. Deformation due to full lateral Water pressure

83

Fig.9.9.Deformation due to half

lateral water pressure

Fig.9.10.Deformation due to wind load

84

Fig.9.11.Deformation due to

earthquake

Fig.9.12.Deformation due to modal

(mode-2)

In the deformed shape due to earthquake loading it clear that the contribution of torsional mode is very

height. The first and second modes which are purely translational have comparatively close period of

vibration to the torsional mode.

85

Chapter 10 Design of Column

10.0. Introduction For the design of columns SAP2000 V18 is used. The design code used is Eurocode-2,2004 with

appropriate NDP (national determined parameter). The table below shown the values used in the design

of column.

Table 10.1. Design values

Table 10.2.Load combination

86

10.1. Design of column

10.1.1. Longitudinal design of column

Based on the Eurocode-2, 2004 the column is designed for both longitudinal and transverse

reinforcement. In this subsection design of column for longitudinal reinforcement will be presented. The

next table shows the longitudinal reinforcement required in mm2.

Fig.10.1. Longitudinal reinforcement

87

10.1.2. Transverse reinforcement

Also the shear reinforcement design is made based on the Eurocode-2, 2004 and the amount of

reinforcement shown in the next figure. SAP2000 gives the shear reinforcement in terms of the area of

shear reinforcement per spacing ( svA

s ).

Fig.10.2. Shear reinforcement

88

For one column detail calculation of the design of column is shown in the next figure.

89

Fig.10.3. Detail design calculation

90

Chapter 11 Detailing

11.0. Container tank detail

a

b

c

d e

f

Bar schedulea Ø12 c/c 90

b Ø32 c/c 100

c Ø8 c/c 90

d Ø16 c/c 100

e Ø36 c/c 100

f Ø16 c/c 100

Fig.11.1. Container Detail

91

11.1. Column detail

6650

5000

5000

5000

4950

700

2000

18

Ø36

14

Ø36

14

Ø36

14

Ø36

14

Ø36

Ø10

c/c

130

Ø10

c/c

130

Ø10

c/c

130

Ø10

c/c

200

Ø10

c/c

200

Fig.11.2. Column detail

92

Chapter 12 Foundation Design

12.0. Introduction

For the design of the foundation of the Intze water tank SAFE 2014 finite element software is used. The

foundation type recommended is mat type with beams and having circular shape. The load on the

foundation is taken from the analysis result of SAP 2000 software and applied on SAFE 2014. The

amount of reinforcement required for the mat foundation as well as for the beam is taken out of the

software. The assumed ultimate bearing capacity of the soil is taken to be 300kPa.

12.1. Modeling

The modeling of mat foundation along with the beams is shown in the next figure. The thickness of the

mat is 800mm where the size of the beam is 400mm by 800mm where 800mm being the depth of the

beam.

Fig.12.1. Foundation Model

At each joint the load is applied taken from SAP2000 output.

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Fig.12.2. Loading Value

12.2. Result

12.2.1. Settlement

The settlement of the foundation under the design load is calculated from the software is shown in the

next figure.

Fig.12.3. Settlement of foundation in mm

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From the result it can be seen clearly that the distribution the settlement of the foundation is even

being the difference between the largest and smallest settlement 6mm only.

12.2.2. Soil pressure distribution

Fig.12.4. Soil pressure distribution

12.3. Design

The design of the foundation along with its beam is done using the finite element software. The results

are displayed in the next figure. The amount of reinforcement can be converted to a spacing using the

appropriate formula.

12.3.1. Mat reinforcement

The amount of mat reinforcement for both direction is given in below again for both top and bottom

sides.

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Fig.12.5.Reinforcement in X-direction

(Bottom)

Fig.15.6.Reinforcement in X-direction

(Top) Use ø20 c/c 150mm Use ø24 c/c 120mm

Fig.12.7. Reinforcement in Y-direction

(Bottom)

Fig.12.8.Reinforcement in Y-direction

(Top)

Use ø20 c/c 150mm. Use ø20 c/c 120mm.

12.3.2 Beam Design

The beam is designed for both flexure and shear in SAFE 2014. The flexural reinforcement is given in

terms of mm2 and the shear reinforcement is given as ( svA

s ). The next two figures will provide the

amount of reinforcement required for the mat and beam.

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Fig.12.9. Flexural reinforcement of beam

Fig.12.10. Shear reinforcement of the beam

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Discussion:

1) The ring beam will be subjected to zero hoop stress when the tank is full. Horizontal

thrust is taken by a rib encircling the edge of the roof dome is provided .A ring beam is

provided to transmit the load to the columns which is provided at the junction of domed

bottom and conical potion.

2) Sloshing wave height is assumed small, it results additional hydrodynamic pressure.

Sloshing is defined as the periodic motion free liquid surface in partially filled containers.

It is caused by any disturbance to partially filled liquid containers.

3) Intze tanks are extensively used for storing water for civic purposes because of their

optimal load balancing shape.

4) Hoop tensile force will mostly govern the thickness of conical and cylindrical walls. The

thickness of spherical bottom dome will be governed by the maximum compressive

stress of the meridonial compressive force and bending moment at the edge.

5) Due to many degrees of redundancy, Stress analysis of Intze tanks is extremely

complicated however with certain approximations the elastic theory of thin shells were

used to analyze these tanks with sufficient accuracy.

6) The principle stress system had obtained using the membrane theory of shells. Stresses

in an Intze type tank due to primary loading using elastic theory. Secondary stresses due

to shrinkage, temp variation and wind forces should also calculate for critical designs.

7) In the Intze tank the various components of the tanks shall be checked from the various

perspectives. Let us start with the dome which is usually provided with thickness of 100

to 150mm and reinforcement must be laid along meridonially and latitudinal. Here the

hoop stress is less than 1.5 KN/m2. Therefore the top dome for the thickness of 150 mm

minimum reinforcement must be provided. Ring beam which supporting the dome is

necessary for resisting the horizontal thrust developed by the dome, therefore this

beam is to be designed from the hoop tension. Below this ring beam cylindrical walls are

there, they should be designed for hoop tension caused by the water pressure. In the

flow of loads the next is the ring beam at the junction of cylindrical walls and the conical

wall; therefore it is to be designed for hoop tension. Basically it provide resistant to the

horizontal component of the reaction of the conical wall on the cylindrical wall. Here

larger width of the beam will serve the purpose of walk way around the tank. It is the

conical slab in next which is also to be designed from the hoop tension point of view.

Basically it is to be designed as slab which is spanning ring girder at the bottom and the

ring beam at the top. The last part in the tank system which is connecting the tank

portion with the staging part that is ring girder that means it is supporting all the tank

and its components. Finally it is resting on the columns therefore it is to be designed

from bending moment and torsion point of view. Columns which transfer the load are to

design from the gravity loads and wind load.

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8) Based on the type of force acting in the member, the member should satisfy the various

types of requirements.

a) Members subjected to axial tension only: In this condition the member should

satisfy the requirements. There should be sufficient reinforcement to resist all the

tensile force. Assuming that the concrete is un cracked and reinforcement act

together to resist the direct force, the calculated tensile stress in concrete should

not exceed the maximum permissible stress in concrete in direct tension.

b) Members subjected to bending moment only: Neglecting the concrete in tension

zone, the compressive stress in concrete should not exceed the permissible value

and tensile stress in steel should not exceed the permissible values. Assuming

concrete to be uncracked the tensile stress in concrete should not exceed the

permissible tensile stress in bending. For cracked condition the usual procedure of

designing singly reinforced beam (or doubly reinforced beam if required) will be

followed here but with the reduced stresses in steel reinforcement. For un cracked

condition, in this case assume that the whole section is resisting the moment and

calculate the maximum tensile stress in concrete which should not be more than

permissible value.

c) Members subjected to combined axial tension and bending: For the members

subjected to combined axial tension and bending moment. It requires for no crack

condition that the stresses due to combination of direct tension and bending

moment shall satisfy the following condition.

Calculated direct tensile stress in concrete

- Permissible direct tensile stress in concrete

Calculated stress in concrete in bending tension

Permissible stress in concrete in bending tension

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Conclusion:

1) About 70% of liquid mass is excited in impulsive mode while 29.5% liquid mass participates in

convective mode. Sum of impulsive and convective mass is 1136410 kg which is about the total

mass of liquid in the earth quake analysis.

2) Finally the earth quake forces are governing the design of the elevated water tank.

Future scope of the work:

i) The Intze tank cost estimation can be done

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Appendix-A

Moment coefficients in circular girders supported on columns:

No of columns

Positive bending moment at center of spans

Negative B.M at support

Maximum twisting moment

Angle between columns

Angular distance for maximum torsion

N K2 K1 K3 Degrees Degrees

4 0.0176 0.0342 0.0053 19022’ 90

6 0.0075 0.0142 0.0015 12044’ 60

8 0.0041 0.0083 0.0006 9033’ 45

10 0.0023 0.0054 0.0003 7030’ 36

12 0.0014 0.0037 0.00017 6015’ 30

Table13.0. Moment coefficients

Source: Ramamrutham.S, 1978, design of Reinforced concrete structures, 8th edition,

DanpathiRai publications.

101

References

1) ACI 350.3-01 and Commentary ACI 350.3R-01.(2001) “Seismic Design of Liquid-Containing Concrete Structures” Reported by ACI Committee 350 Environmental Engineering Concrete Structures, 350.3/350.3R-1

2) American concrete institute (ACI) code

3) BIS Draft code on IS: 1893-part 2, “Criteria for Earthquake Resistant Design of Structure, Liquid Retaining Tanks Elevated and Ground Supported (fifth revision of IS: 1893)”, Workshop on Revision of IS Codes on LRS.

4) Charles.N. Gaylord, Edward.H.Gayurd.Jr, and James. E.Stall Meyer, Structural

engineering handbook, 4th edition

5) Dr.H.J.Shah, Reinforced concrete vol-II (Advanced Reinforced concrete) Charotar

Publishing house Pvt. Ltd.

6) Dr. Shah H.J., (2012), “Reinforced Concrete Vol-II”, Charotar Publishing House Pvt. Ltd.,

Anand, Gujarat, India.

7) Dutta, S.C., Jain, S.K. and Murty, C.V.R., (2000). “Alternate Tank Staging Configurations

with Reduced Torsional Vulnerability”, Soil Dynamics and Earthquake Engineering 19,

pp.199–215, “Assessing The Seismic Torsional Vulnerability of Elevated Tanks with RC

Frame Type Staging”, Soil 7.Dynamics and Earthquake Engineering 19, pp.183–197.

8) Dutta S.C., Jain, S.K. and Murty, C.V.R., (2001), “Inelastic Seismic Torsional Behavior of Elevated Tanks”, Journal of Sound and Vibration 242(1), pp.167

9) Ethiopian building code of standard (EBCS) -1,1995



12) Eurocode-2 2004

13) Eurocode-8 2004

14) Falguni, A., and Vanza, M.G., (2012). “Structural Control System for Elevated Water

Tank”, International Journal of Advanced Engineering Research and Studies.E-ISSN2249–

8974.

15) Federal Emergency Management Agency, FEMA 273, (1997), NEHRP Guidelines for the

Seismic Rehabilitation of Buildings and in furtherance of the Decade for Natural Disaster

Reduction.

16) Housner, G. W., (1963), “The Dynamic Behavior of Water Tanks”, Bulletin of The Seismological Society of American. Vol.53, No.2, pp.381-387.

17) IS 3370-2009 code of practice for concrete structures for storage of liquids. 18) James. E. Amrhen, Reinforced Masonry engineering handbook, clay and concrete

masonry, 5th edition, CRC Press. 19) Pillai, TATA Mc.Grahill, Reinforced concrete design, 3rd edition. 20) Robert.W.Day, Foundation engineering handbook, McGraw hill construction ASCE Press. 21) SAP 2000 manual

22) W.F.Chen, hand book on structural engineering, CRC Press.

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